The 21-year-old has signed a deal until the summer of 2026, subject to international clearance.
Matondo’s transfer to the cinch Premiership runners-up earns him a return to the UK, having spent his early years at Manchester City before leaving three years ago to sign for Schalke.
“I am absolutely buzzing to have signed for a club as big as Rangers,” he told the club’s official website.
“I am just looking forward to getting on the pitch at Ibrox in front of the amazing fans we have here at Rangers and I am excited.
“This is a big club with a massive history and I just want to create more memories and more history here at the club.”
Forward Matondo has struggled to find a permanent home since he departed the Etihad Stadium in 2019.
The Liverpool-born winger managed to force his way into the Schalke squad during his first couple of seasons but has spent the last two campaigns on loan at Stoke and Cercle Brugge respectively.
Rangers boss Giovanni van Bronckhorst is excited to work with the youngster, and added: “I’m really pleased to welcome Rabbi to Rangers.
“I spoke last week about my desire to add more attacking quality to my squad, and we all believe Rabbi will do that.
“He will bring many strong attributes to the team and I am really looking forward to seeing him in training this afternoon for the first time.”
Matondo is the fourth player to move to Ibrox this summer after John Souttar, Antonio Colak and Tom Lawrence.
Sporting director Ross Wilson said: “We have been quietly working to secure Rabbi’s signature for the last few weeks since the June internationals finished.
“We wanted to invest in a wide player this summer and we are excited with what Rabbi will bring to our group, with his speed and his general style of play.
“At 21 there’s lots more to come from Rabbi and he will be a strong investment and addition to our group.”