Would the phrase “No worries!” be understood outside Australia?

In Australia, No worries! is a very common way of saying You’re welcome.

I wonder whether it is used this way in other English-speaking countries.

The phrase’s meaning can be understood easily enough in context, so it should therefore be safe to use, but I’m still curious whether it would sound natural to non-Australians.

In England (and Britain generally, I think) it would be seen as definitely Australian. Not a bad thing, of course, but not 'natural' in your sense.

That phrase is common here in New York City. It is a more relaxed way of saying you’re welcome.

It's not as prevalent as in Australia or New Zealand, but you do hear it in the US. I have certainly heard it in Texas.