Brobbey had a disappointing season last year, scoring only three goals in 30 Eredivisie matches. He ended his Ajax career with 163 games and 56 goals. This season, he suffered a knee injury in the preseason and has not played yet.
Ajax had been in talks with Stade Rennes, but Brobbey did not want to move to France. At Sunderland, he will compete for a spot in the starting lineup with Eliezer Mayenda and Wilson Isidor.
Brobbey joins fellow countrymen Robin Roefs and Lutsharel Geertruida, who joined the Black Cats on loan from RB Leipzig earlier on Monday.