In certain situations, yes, but 大丈夫 is an adjective, while "no problem" is not.
Well, in the 3rd entry for 大丈夫 it actually appears "that's alright" which sounds pretty close to "no problem" to me.
I'd think that wouldn't work really. I'm still studying though so I dunno
I think people are getting too technical about this...
Yes, originally, 大丈夫 is an adjective used to describe something that is "okay."
But colloquially (and probably more commonly used), it can definitely be interpreted as "No problem," as in, "(the situation is) no problem!" or "not a problem."
Languages are complex and when it comes to Japanese, there's a lot of flexibility in its interpretation.
TL;DR - Your definition for 大丈夫 is 大丈夫!
@SwimmingBird, you are aware that the original post is 7 years old, aren't you?
"No problem!"?
Wouldn't "No problem!" be a nice translation, too?