The 20-year-old forward has joined from West Brom on a three-year deal. The former Celtic academy player endured an injury-hit loan spell at Motherwell last season, which ended before he could make a league appearance.
“We had been speaking to West Brom about a loan initially, but when the chance came to do a permanent deal we were really excited about it because the more permanent deals that we can do and develop our squad for the future, the better,” McLeish told St Mirren website.
"Eseosa came up on loan to Motherwell last year and was unfortunate that he picked up an injury and had to head back down the road without really featuring much.
“But he's one that we're excited about because it gives us the bit that we're looking for where he can stretch defences. He gives us a real threat and speed in behind."