The outside diameter of Glock .40 and .357SIG barrels are exactly the same. All Glock did when they made their .357SIG models was to re-chamber the existing .40 barrels, add a little more metal to the .40 frames, and change the magazines slightly.
If your G22 is Gen3 or Gen4, you can do it. If it's Gen2 you'd need to call Glock and ask them if that particular serial number's frame has enough metal reinforcement to shoot .357SIG. Sometimes they'll tell you yes or no, other times they'll tell you a blanket statement to only shoot the caliber it was originally chambered in for liability reasons.
Early Gen2 .40 frames didn't have enough metal reinforcement to handle .357SIG. The extra metal that was later added extended off of the front frame rail insert to stop frame battering, and the rear frame rails were lengthened as well. Later Gen2 .40 frames will have the necessary reinforcement but the only way to know is to ask Glock and hope they're willing to tell you. Gen3 and Gen4 .40 and .357SIG frames are identical between each caliber, they have the proper reinforcement. You can't necessarily judge by the length of the rear frame rails because the early production Gen3 rear frame rails were longer, newer production were shorter but made of a stronger steel.
You may need to use .357SIG magazines for 100% reliability but most people say the .40 magazines work fine. The inner dimensions of the magazine tube and the followers themselves are different between calibers. All of the other internal parts work for both calibers so there's no need to change anything else.
www.glockmeister.com - Tech Info