The 30-year-old passed a medical at Ewood Park and agreed personal terms on a three-year deal and will link up with his former boss at Liverpool, Graeme Souness.
Leeds Chief Operating Officer Shaun Harvey said on the official website: "I would like to thank him on behalf of everyone at Leeds United for his efforts whilst at the club and we wish him every success in the future."
Matteo made 146 appearances in all competitions for Leeds, scoring twice in Europe and twice in the Premiership.
Souness said: "Dominic is a proven player with an impressive track record and I am delighted to have him on board. He is versatile, able to play a couple of roles both in defence and midfield, and that is an important feature."