The Turkish international duo were both officially unveiled in a signing ceremony held at the Şükrü Saracoğlu stadium.
Tufan signed a five-year contract while Şen put pen-to-paper on a three-year deal.
The Yellow Canaries have now completed four signings from Bursaspor this season including last seasons top league scorer Fernandao and right-back Şener Özbayraklı.
Tufan rose to prominence last season at Bursaspor under the stewardship of current Beşiktaş manager Şenol Güneş.
The 20-year-old rose from total obscurity into a house-hold name in Turkey and a Turkish national team regular.
Bursaspor reached the Turkish Cup final last season and scored the highest number of goals in the league – 66.
Tufan scored three goals and provided nine assists in all competitions for Bursaspor last season.
Volkan Şen meanwhile scored an impressive 17 goals and provided 12 assists for the Green Crocodiles in all competitions.