The 25-year-old struggled in his first campaign as Bayern's number one last term and lost his place to Hans-Jorg Butt towards the end of the season.
Bayern were linked with a move for Schalke's Manuel Neuer earlier this summer, but coach van Gaal is prepared to put his trust in Rensing.
He played in Bayern's 3-1 DFB-Pokal win over sixth-division side SpVgg Neckarelz on Sunday.
"I have watched for four-and-a-half weeks and now have made my decision," Van Gaal said on Bayern's official website.
"I am putting my faith in Michael Rensing."
Rensing added: "We have both had a good pre-season, so I am luckier that I have been chosen. I have believed in myself and my abilities."
Manuel Neuer Girlfriend Images
