You want to wait until the cat has accepted that this is its new home. How long that takes depends on the cat; it was a month before my two decided I was an acceptable human, and they're indoor cats.
One thing I used to do with outdoor cats after moving was to go out with the cat the first few times -- walk them around the building while they check out the neighborhood and landmarks. They seem to like knowing I'm there if the run into something which might object to them.
Make sure the cat has a collar with your phone number, so if it does get lost or hurt people know who to call. The collar is also an immediate signal that this is a pet rather than feral, which is sometimes important. Ideally the collar should be elastic or have a break-away link so the cat can escape if it gets snagged on a branch, but mine always wore traditional collars and never had a problem (outside of the initial argument about "you are not going out of the house naked, young lady!"). I've also found the collar a useful signal to the cat about whether it will be allowed out or not.