I've just had a set of rims painted - Gotta love Birthdays & Fathers Day.
They currently have no tyres on them.
I have heard that paint can be "soft" for a while and it may be wise to leave them alone for a while so the tyre fitting and/or road use, doesn't damage/scratch/chip the new fresh paint.
Does anyone know how long should I wait before fitting tyres and fitting them to the car?

It will depend on whether the paint used is lacquer based or turps based...if the former then a few days should be ample, but if turps based and more than one coat has been applied then I'd personally leave it for a fortnight...probably in the sun to heat it up and aid the drying.
The job will be better if the rims were stripped to bare metal as this improved adhesion. Most of the tyre shine preparations leave a residue on the rim that is very hard to remove unless stripped.
Good Luck and happy birthday.