The 23-year-old shot-stopper joins the Rockets from Nigeria Premier Football League champions Remo Stars.
He has signed for Galaxy on a free transfer and joins fellow foreign signings Tape Ira, Igor Salatiel Silva, Paulo Martins Filho, Mory Keita and Mehdi Ouamri at the club this season.
Bankole is joined in the South African top-flight by fellow Nigerian goalkeeper Stanley Nwabali, who plays for Chippa United.
Galaxy announced the news with a post on social media.
"Welcome to the family, Kayode Bankole!," the club posted.
"A commanding presence between the posts and a true game-changer joins our ranks.
"We can't wait to see you showcase your talent and passion on the big stage!"