The pair became Sunderland's 12th and 13th captures of the transfer window, the English Premier League club said on their website (www.safc.com).
Striker Borini, 22, joined Liverpool from AS Roma a year ago but foot and shoulder problems limited him to 12 league appearances for the five-times European champions.
He has previously played for Chelsea and Swansea City and has been capped once by Italy.
Left back Dossena, 31, joins Sunderland from Napoli on a one-year deal.
Former Liverpool defender Dossena, who has won 10 caps for his country, made 24 appearances last season as he helped the Italian club finish second in Serie A.
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