The two join part of an emerging Italian contingent under manager Paolo Di Canio at the Stadium of Light.
The two players become Paolo Di Canio's 13th and 14th signings of the summer in what has proven to be a radical overhaul of the playing squad at the Stadium of Light.
Borini has struggled to nail down a starting spot at Anfield and - following the January signings of Philippe Coutinho and Daniel Sturridge, along with Iago Aspas' arrival - the 22-year-old's first-team chances this season looked limited.
Napoli purchased the 31-year-old Dossena from Liverpool in 2010 but the wingback has struggled at the Stadio San Paolo and spent part of last season on loan at Palermo.
Di Canio swooped for his fellow countrymen after Dossena's reported move to Torino broke down and after being alerted to Borini's availability, as they joined the Black Cats' increasing Italian contingent. Vito Mannone and Emmanuele Giaccherini joined the club earlier in the transfer window.