The 21-year-old is the eighth signing made by the Stadium of Light club since they recruited Jack Ross as their new manager.
Sunderland were relegated to League One this past season, which means they are determined to bounce back into the Championship.
Speaking about his new signing to safc.com, Ross said: "We need more players in the forward areas and Jerome is somebody who fits into that bracket.
"He can play in multiple positions across the front line. I'm pleased to get him in and he's at a stage in his career where he needs to play games.
"He's hungry to prove himself and he's got a big opportunity here to do that."