For a non-native English speaker, it seems that "air" is a noun and "conditioned" is an adjective. Following the correct word order, the adjective should precede the noun, so it should be "conditioned air". So why "air conditioned"? Are there other examples of the same word order?
I think we feel like "air condition" is a verb. "I'm gonna air condition the place" is a real sentence. Subject: I. Verb: air condition. Object: place. So the gerund is "air conditioning" "He was air conditioning the place". And, the participle is "air conditioned".
As to your point that "air" is a noun and "conditioned" is an adjective, I would like to explain that English, being a Germanic language in part, has some Germanic habits, one of which is to use a noun as an adjective. This should not be overdone, but one sees it a lot. Thus "toilet paper" versus "paper toilet". In the former, "toilet" is being used to tell you what kind of paper. it is being used adjectivally. In the latter, "paper" is being used to describe what kind of toilet it is: one could, in theory, build a toilet out of paper...although paper mache might be better.
It may be helpful to consider a sample sentence:
An air-conditioner pumps conditioned air into what is therefore an air-conditioned building.
Now let's break it down:
- Air-Conditioner: The unit of machinery which conditions the air.
- Conditioned Air: The air-conditioner takes in untreated air and treats (conditions) it. The output is therefore air that has been conditioned, or "conditioned air".
- Air-Conditioned: Used as an adjective to describe the air in the building as being treated via air conditioning as opposed to a building which is not.
English as German heritage is indeed part of it, but....
Willis Carrier came up with the method for conditioning air, not only cooling it, because both humidity and temperature together were changed. Since the machine conditioned air, it was natural to call it an "air-conditioner", and the process "air-conditioning", in keeping with the established practice of so pairing objects and verb-derivatives: physics teacher, piano-player, meat-cutting, paper-hanging, woodchopper, woodcutter, egg-slicer, and many others. With the prevalence of the compound over the constituent parts, many naturally, as aforesaid, take the compound for a solid verb-derivative, as if there is a verb "air-condition"—and then, therefore, there is, and something can be "air-conditioned".
Now, English is not agglutinative, and expressions such as "conditioned-aired" or "conditionedairy" (with conditioned air), or "airconditioningy" (with air conditioning) do not happen.
The OED lists as the earliest attestations of the nouns air conditioning and air conditioner the following two citations from the same 1909 source that discusses cotton manufacturing (my emphasis):
p. 1395: *I finally hit upon the compound word, ‘Air Conditioning’... Suggested by the use of the term ‘Conditioning’ in the treatment of yarn and cloth.
p. 1411: Well-known ‘Air Conditioners’ of both individual and central station types.
Obviously, the author uses the expression air conditioning because the unmodified expression conditioning was already used in related contexts. He later coins the term air conditioner to refer to the machines doing the conditioning. By the end of the 1930s, this noun appears to be already in fairly common use (OED, my emphasis):
1937: Air conditioners have been designed to supply fresh air, and to maintain a comfortable cabin temperature while a machine is on the ground.
Note that both nouns follow the typical structure of compound nouns in which the first element is a syntactic complement to the deverbal second element: air conditioning is equivalent to "to condition air"; air conditioner is equivalent to "something that conditions air". Obviously, the order of the two elements in the nouns is fixed.
The first attestations of the adjective air-conditioned and the verb to air-condition in the OED are from several years later than air conditioner or air conditioning (my emphasis):
1937: Delco Conditionair for forced warm air systems. ‘It air conditions as it heats.’
1927: Hotel, new Frigidaire air conditioned.
1932: Certain special considerations such as the necessity of refrigerated or air conditioned storage.
It's noteworthy that the 1927 and 1937 citations refer to particular brands of air conditioners – and that the brand names themselves play on the near-homophony of air and the agentive suffix -er that was used to form conditioner.
What this seems to suggest is that the concept of an apparatus that treats the air in a room was already well established at the time, and the noun air conditioner was commonly used to refer to such an apparatus at the time the verb and the adjective were formed. The OED also suggests this etymology: the 1909 air conditioner is argued to have been formed on the basis of the form air conditioning from the same publication. Both the verb air-condition and the adjective air-conditioned are argued to be based on the earlier nouns.
So, the verb and the adjective exist in their present form because they were based on a pre-existing noun and retained the word-order from that noun. Subsequently, they became lexicalized to refer to a very particular concept: the process of using an air-conditioner or to the property of having been submitted to air-conditioning, respectively. This is different from conditioned air or to condition air – these expressions don't have the particular, lexicalized meaning that the former carry.
I believe it's because "air-condition" is being used as a compound verb (which happens to be a hyphenated word), not a separate noun and verb. Note that compound verbs usually have hyphens.
It's also a verb being used as an adjective, but I think we already knew that.
"This machine air-conditions the building." is a valid sentence. Here, "air-condition" is the main verb in the sentence.
"This building is air-conditioned." is also valid. Here, it's used as an adjective.
"This machine is an air conditioner." - also valid. "air conditioner" is a compound noun. It's a thing which conditions air.
"This machine supplies conditioned air to the building." - also valid.
"This building has conditioned air." - valid, but unusual. It says that the air in the building is conditioned.
"This building is conditioned air." - definitely wrong. If you can't say "the building is air", then you also can't say "the building is (adjective) air", which just adds more detailed information about the air.
Many native speakers are sloppy with punctuation. "air conditioned" is just "air-conditioned" without the hyphen.
We talk about air conditioners, which cost money and break down, and air-conditioned buildings, which are nice to sit in, much more often than we talk about the air itself.
Back when air conditioning was new, people could have decided to say "a conditioned-air building", meaning "a building whose air is conditioned", but they didn't. English compound adjectives can use the "adjective + noun" format - for example, "a big-screen cinema".
Let's pretend that "conditioned-air" was the correct adjective. In that case:
"This is a conditioned-air building." - OK.
"This building is conditioned air." - still wrong. The building is not made of air.
"This building is conditioned-air." - Not wrong, but unusual. Compare: "This cinema is big-screen." instead of "This cinema has a big screen." or "This is a big-screen cinema."
The expressions "air-conditioned" and "conditioned air" have different meanings. "Air-conditioned" means "conditioned with regards to the air" and in this case "air" adds detail to which respect something has been conditioned for. In this usage, the noun becomes somewhat integrated with the adjective to add detail to it. Similar examples are "speech-impaired", "ironclad", footloose". When building such constructs it's important to separate noun and adjective with an hyphen, unless they are of common use. User Toby Martels noted: "once a hyphenated compound is used so commonly that people no longer think of it as made of its constituent parts, then it loses its hyphen."
To further complicate the issue- "conditioned air" is a bona fide term and used in the HVAC industry: https://en.wikipedia.org/wiki/Air_handler
Generally it describes the state of the air in the process- you have make up air that comes in from outside, you have 'chilled' air that has been dewatered (humidity removed, bone dry), you have cross-flow heat exchangers...
But your question was why, and so if you were in the hVAC industry talking about states, you'd probably utilize 'conditioned air' to describe air being moved through the ductwork to a space to be conditioned.
I hope I haven't confused you too much, but the wiki link goes into further detail.