The 26-year-old, who has joined Saints on loan until January, was a team-mate of Inverness Caledonian Thistle's Boyce while the pair were at Cliftonville.
"If you look at his career stats in the Irish League, he's scored a lot of goals," Wright told his club website.
"He's also a former team-mate of Liam Boyce, who has done well up here."
Fellow Northern Irishman Wright stressed: "They are different types of players, but Joe has the potential to do well."
Gormley had joined Peterborough from Cliftonville last summer, but he has made only seven appearances for the English League One side - one this season after recovering from a knee injury picked up in September.
"He's coming back off a significant injury, but he's fully fit and trained with us this morning," added Wright.
"I'm delighted to get a striker in.
"Joe is a player I've known from his time at Cliftonville and we were interested in him back then, but he went to Peterborough."
St Johnstone manager Tommy Wright hopes Joe Gormley will make as big an impact in Scotland as Liam Boyce after signing the Peterborough United striker.