The Bones spinoff, which will air on Fox in midseason, stars Geoff Stults as an Iraq veteran called Walter with an ability to locate people and things.
Masöhn and Hasson have now joined the show to fill the gap left by departing cast member Saffron Burrows, TV Line reports.
Masöhn will star as Isabel Zambada, a deputy US marshal who has a "vigorous friends with benefits" relationship with Walter.
However, Isabel is ambitious and hopes to become Attorney General, and may become concerned that Walter could hold her back.
Masöhn has previously appeared in episodes of shows including Chuck, Traffic Light, Common Law, Castle, The Closer and Entourage.
Meanwhile, Hasson - a 16-year-old newcomer - will play Willa, a girl born into a family of criminals. Willa, who is described as "manipulative, cynical and extremely bright", is out on parole and ends up helping Walter and Leo (Michael Clarke Duncan) with their work.
The Finder is expected to premiere in January.
Watch a trailer for The Finder below: