The 21 year old has 1 cap for Scotland and may prove handy on the end of crosses since he stands at 6"1.
"We are very happy to get Paul," Stoke's director of football John Rudge told the official website.
"He is a young striker of potential and we think he can do a very good job for us in The Championship.
"We came very close to signing McEveley as well, who would have given us extra defensive options, but he decided at the last minute to go to Ipswich."