Re: For clarity and cleanliness, I'd recommend...

[xdg]

Given how often I hear about (even experienced) programmers mistakenly typing "=" in an if statement when they meant "==", I don't know if encouraging this particular idiom as a rare case where it is indeed what you mean is a good idea. Might I suggest this instead:

while (my $result = thatroutine()) {
     return $result;
}

As an aside, I was actually surprised that the version with if didn't warn about the single "=", but a little testing showed that the warning only appears to happen if you mistakenly assign (instead of compare) a literal value, not a subroutine.

[TheDamian]

I agree with you. I would certainly never recommend that people write:

if ($result = thatroutine()) {
     return $result;
}

But, as your while-based variant shows, non-constant assignments in a conditional are always fine if you're declaring the lvalue variable at that point:

if (my $result = thatroutine()) {
     return $result;
}

In such cases, the = must be intentional, since == on a newly-created variable doesn't make any sense.

As for your alternative suggestion, I don't feel it's a clear or as clean as using an if, because the use of a while implies looping behaviour, which the return undermines in a not-entirely-obvious way. That could be especially misleading to subsequent readers of the code if the number of statements in the while block later increases, pushing the return away from the loop keyword it's subverting.