Whenever you ask this person for his motivation for doing something or why he thinks something etc. you'll get an immediate response along the lines of "no reason/there is no meaning to it."
It depends on whether you have a generally positive attitude toward the person/characteristic and think he has a good character or whether you have a generally negative attitude toward him or the characteristic and think he's got a poor character. I think you can see from the answers here that people pick one or the other.
Positive: whimsical, carefree, easy-going, light-hearted, mellow, unassuming
Negative: unmotivated, listless, careless, unfocused, devil-be-damned
If he was doing something to the benefit of someone else without their knowledge (and without seeking praise from anyone else) you could call it an altruistic act.
Or take a philosophical approach - describing them as an existential nihilist would be a good place to start.
I honestly don't believe there is a word in English for someone who always says he is doing something without a/for no reason.
But it's a very adaptive language. Feel free to make up one of your own. I'll personally use it a the very first opportunity.
I'm trying to think of some equivalent in Yiddish we could use but it escapes me. Someone help here, please?