Tubbs joined Rovers from Portsmouth on a one-year deal in July, making nine league appearances before joining Woking on loan in September.
The 32-year-old scored three goals in six games for the Cards, before playing two more games for Forest Green.
"This is a superb signing for the club. Matt has a proven record at this level," Sutton boss Paul Doswell said.
Sutton have signed striker Matt Tubbs from National League rivals Forest Green Rovers on a permanent deal.