Jessie enjoyed two loan spells last season spending the first half of the campaign with Portsmouth, scoring five goals in 15 games, followed by four goals in 12 appearances with Bristol City.
The striker has represented England at all youth levels up to Under-23s.
Gale said: “I’m just so happy to finally be here and be part of such an ambitious club. This is not the type of club that you turn down. When I heard about it, it was a no-brainer.
“As a striker, I want to score as many goals as I can. I want to get promoted with this team, that is why I came here.”