The speedy kick returner/receiver signed a contract extension with the CFL club Thursday that will keep him in Hamilton through the 2017 season.
Banks was scheduled to become a free agent Tuesday.
The five-foot-seven, 153-pound Banks led the CFL in combined yards (1,968) and punt return yards (618) and was third in kick-return yards (701) en route to being named a league all-star.
The 27-year-old international player also had 42 catches for 529 yards and tied for the team lead with five receiving TDs.
Banks had a CFL playoff-record 226 punt return yards in Hamilton's 40-24 win over Montreal in the East Division final. He also tied a league mark for punt return TDs in a post-season contest with two.
Banks had a 90-yard punt return TD nullified by a penalty late in Hamilton's 20-16 Grey Cup loss to the Calgary Stampeders on Nov. 30 at B.C. Place Stadium.
"Brandon is one of the premiere playmakers in the league with the ability to change the game every time he touches the ball," Hamilton coach/GM Kent Austin said in a statement. "We are extremely happy that he will be with our team for the next three years."