Dossena became Sunderland's 14th signing of the summer when he joined Paolo Di Canio's side on transfer deadline day from Napoli.
The former Liverpool defender came close to joining Torino earlier in the transfer window, but reportedly failed a medical due to a thigh injury.
Despite the move falling through, Dossena is looking forward to be playing in the Premier League again and is confident he will be back to full fitness in the next couple of weeks.
"I am pleased to return to the Premier League - it's the most-watched league in the world and the atmosphere is nice and warm," Dossena told Radio Marte.
"My injury will last a fortnight, so I will soon be available. Torino? I have no regrets, they needed a player who was ready to play straight away."