He was one of their best in their tight opening wins over Manly and Penrith.
Melbourne Storm football director Frank Ponissi said the club was thrilled to have re-signed Bromwich.
"Jesse's signing is terrific news for Melbourne Storm, it's another great announcement for the club and a key part of our retention strategy,'' Ponissi said.
"Jesse has progressed into an elite footballer who also has shown his leadership potential.
"He's a big guy with good footwork and is very consistent.''
Utility Griffin, 23, made his NRL debut in round one last year and managed six games for the season.
Meanwhile, Munster, 19, made an eye catching debut during Storm's trial matches.
The Queenslander, part of the club's NYC team, is tipped to be next Billy Slater.
- AAP