Hamburg have snapped up Olympic champion and Brazil international Walace from Gremio for a reported EUR10million, while Eduardo Vargas has agreed an exit from Hoffenheim.
Walace, 21, has signed a contract that runs until 2021 and will begin training with his new team-mates on Tuesday.
Walace helped his country to their first Olympic gold in men's football at Rio 2016, playing a part in Gremio's Copa do Brasil triumph upon his return to club duty.
Prior to those achievements the midfielder was a surprise inclusion in Dunga's Brazil squad for the Copa America Centenario last June, and his burgeoning career began a new chapter on Monday.
Walace said: "I am very happy to be here in Hamburg. What is important is that I get used to the new situation quickly, so I can show a good performance on the pitch. I hope I can help the club in the current difficult situation."
Hamburg are 17th in the Bundesliga, three points adrift of safety. However, sporting director Jens Todt warned against lofty expectations being placed upon Walace.
"Walace is physically strong and a powerful player. We are very pleased that he now plays for Hamburg," said Todt.
"We want to help him to make the transition as easy as possible, but we cannot expect too much from him right at the start of his time in Germany, and we will treat him fairly and give him time to adapt."
Chile international Vargas' completed a move to Mexican champions Tigres after a largely unsuccessful spell at Hoffenheim.
The 27-year-old forward scored just twice in 29 Bundesliga appearances for the club.