Should be no problem at all, the nut slots are almost certainly going to be wide enough to take 10s. If you went to much heavier strings the slots would probably need widening.
You might need to tweak the setup though - if the Strat has a floating trem you'll definitely need to tighten the springs a little, the intonation will probably need a slight adjustment and you might need to tighten the truss rod a weeny bit.
All very minor adjustments though - it'll play OK if you just stick the 10s on and leave everthing as it is, for now. :)