The 28-year-old signed a four-year-deal in the club's premises in Bursa on Monday.
Bursaspor executive Necmettin Kocaman said they were glad to sign a star like Dzsudzsak and claimed that their new player is one of the biggest talents in Hungarian football.
During his career Dzsudzsak played for PSV Eindhoven, Anzhi Makhachkala of Russia and Dynamo Moscow.
The Hungarian international scored seven goals and produced 13 assists in 43 appearances for Dynamo Moscow last season.