It sounds a lot more nuanced than a simple 'goodbye'. What subtle feelings or emotions does it encapsulate?
As far as I know it is not commonly used. In fact it sounds so unusual, it was used as a salutation in the 1993 science fiction movie "Demolition Man" (Sylvester Stallone and Sandra Bullock), where people from a sanitized and pacifist future reality would wish each other "be well" instead of "good bye". This excessive congeniality made them sound exceptionally naive.
A more common expression is, "Take care!", even if the person is not about to do anything dangerous.
I started saying this a few years ago. I still use "goodbye" and other idioms, but when I say "be well" I mean something more emotional, deeper. It's my way of saying, "For however long passes between now and when we next see each other I hope you have a good life. Have a joyous life. A prosperous life. A healthy life. The life you most desire. And when we see each other again let us rejoice."
This question is likely a matter of opinion. "Be well" is certainly not a typical departure phrase.
I have sometimes heard this phrase used by people who strive to be alternative (a theme in my community), and use language that is intentionally different from many other people's.
I also just recently saw this phrase used in email and other electronic message signoffs to a friend who has been extremely ill. In this case the phrase could be a wish that the person becomes well, or could be an attempt to avoid saying "goodbye" (again, this is a matter of opinion), which could sound, well, final, or "see you later," when there is a good chance that will not happen.
In Yiddish, the expresssion “Zei gezunt” (“be well”) is very commonly used, and often as a way of saying goodbye. If I had to hazard a guess, I’d say that the usage of “be well” in English as words of parting originated in areas of the US with a large Yiddish-speaking population, and gradually gained wider popularity. Personally, I like the way it sounds — it seems to have a kind of warmth and familiarity to it.
I have been using Be Well for more then 8 maybe even 9 years or more. I don't do goodbye anymore.
I started doing it because good is way to light or dark in the use of words good also does not say much on parting. Be Well handles a lot better, it leaves a lot for the one who hears it to place it on a scale themselves. Take care sounds like their is risk at every turn. Where I would use Be well and safe travels, I am drawing perception to the idea of more awareness when driving or travelling. Or safe journey, also works I may even use have a happy morrow. As in wishing their next day well, but I also tend to let people know when I am leaving to do something else or going to my room so they know they have more privacy when we have shared company.
“Be Well” is an old Hebrew greeting and equivalent to saying good bye, here is a link to what is behind this.