Malik leaves the Reds after making 110 appearances in six seasons, during which he became a cornerstone of Josep Gombau's football revolution.
“We are sad to see Ossie go, but want to thank him for all his efforts with our team," Adelaide coach Guillermo Amor said.
“He is a great person who will be missed by everyone in the club. We wish him well for the rest of his career.”
20-year-old midfielder Mauk goes the other way and will head straight to Adelaide having finished his commitments with Aurelio Vidmar's Olyroos squad in Doha.
“We are very happy to have Stefan joining us,” Amor said.
“He is another South Australia player and this is important to us.
“He is a young, but very talented player with a big future in football. He will fit into our team and our style well.
“We are confident that he can have a big impact on our team and look forward to him being part of our club.”
Meanwhile, former Central Coast Mariners attacker Nick Fitzgerald will join Malik at City, after leaving deciding to leave Gosford.
He adds another attacking string to John Van't Schip's bow and along with Malik is available to make his Melbourne City debut on Monday night against Wellington Phoenix.
“Our focus during this transfer period has been to further support our existing squad members and provide additional depth in key positions,” van’t Schip.
“We believe Osama and Nick add valuable experience, complement the squad and will be welcome additions.
“Meanwhile, Stefan has been a valuable contributor to the club and will pursue another opportunity, for which we wish him all the best.”
Malik and Mauk have signed contracts at City and Adelaide respectively for the rest of this season and all of the next, while Fitzgerald has joined City for the remaineder of this season.