The Belgium international has joined the club for a fee believed to be in the region of £8 million, and is the Reds' fourth signing of a busy summer transfer window
The 25-year-old shot-stopper made 101 appearances in three years for the Black Cats, but has swapped Wearside for Merseyside after penning a "long-term contract" following a successful medical at Melwood.
As reported by Goal, the Belgium international is part of a £42 million transfer splurge by Liverpool, with the club also chasing Henrikh Mkhitaryan following the successful signings of Iago Aspas and Luis Alberto.
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"I am delighted that we have been able to sign one of the top goalkeepers in the Barclays Premier League," Rodgers told the club's official website.
"Simon will join a club that will give him an opportunity to demonstrate and improve his huge talent."
The signing of Mignolet will add further fuel to the speculation linking current Liverpool No.1 Pepe Reina with a move away from Anfield, but Rodgers has previously insisted the Belgian has been bought to provide competition for the Spaniard.
Sunderland boss Paolo Di Canio was sad to lose the young goalkeeper, and thanked Mignolet for his contribution to the Black Cats' survival bid last season.
"Simon is a fantastic footballer, a fantastic professional and a fantastic lad and I would like to personally thank him for his contribution to the team last season," the Italian head coach told the club's official website.
"He was crucial to what we achieved and he goes with the very best wishes of everyone at the club."