Jadon Sancho and Brahim Diaz have already left City for Borussia Dortmund and Real Madrid respectively after failing to break into Pep Guardiola's City squad, with Riyad Mahrez's July 2018 arrival for a then club-record £60m ($78m) fee pushing them down the pecking order.
Guardiola recently praised the youngster for his unique talent, insisting he 'knows how good he is', but the Spanish boss failed to grant him a single Premier League appearance.
Bundesliga English (@Bundesliga_EN) January 30, 2019
"Before coming here I already knew a bit about Schalke: Mesut Ozil, Ivan Rakitic and Leroy Sane all took big steps in their careers here,” said Matondo, after completing his switch to Germany.
"As well as that, I had some good chats with the coach and my new team-mates only had good things to say. The Bundesliga is a great league too.
"Schalke is the right decision for my career and I'm happy to now be a part of this club and their future plans."
Schalke's 33-year-old coach Domenico Tedesco confirmed Matondo had been a target for some time.
"We have been interested in Rabbi for a long time, because we are impressed with his potential," he told Schalke's website.
"He is extremely quick and technically strong. We can't forget how young he is though.
"We will give him the time he needs to find his feet at Schalke and in the Bundesliga."
Sancho has made a stunning impact since leaving City for Dortmund, helping his new club top the Bundesliga and breaking into the England team, while Diaz has made one brief appearance off the bench in La Liga since joining Madrid for a reported €15m ($17m, £13m) fee this month.