The Belgium international has penned a "long-term" contract at Anfield after passing his medical.
The 25-year-old has impressed in the north east since arriving from Sint-Truiden in 2010, establishing himself as one of the most promising keepers in Europe.
"It's a big club and when you arrive it's a big thing," Mignolet told liverpoolfc.com.
"I'm very pleased to be here and I'm looking forward to getting started.
"The first training [session] will be very early and I'll be happy to be there.
"I think it will be very special the first moment I step onto the pitch."
Mignolet is confident he can fit in with Rodgers' passing philosophy, which starts with the goalkeeper.
"Back in Belgium, the goalies always train to play with the ball at their feet," he added.
"We join in most of the time, playing more with our feet than with our hands. I'm used to this.
"I've spoken to him [Rodgers] a few times already and I'm very pleased. He is very ambitious, like I am.
"Let's hope we can win a lot of games and finish as high up the table as we can."
Mignolet becomes Liverpool's fourth signing of the summer following Manchester City's Kolo Toure, Celta Vigo's Iago Aspas and Sevilla's Luis Alberto.
Sunderland boss Paolo Di Canio thanked keeper Mignolet for his efforts as he prepared to launch a new era at the Stadium of Light.
Di Canio promised the proceeds of the move would help his ongoing mission to re-shape the squad he inherited from predecessor Martin O'Neill.
The Italian told the club's official website, www.safc.com: "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.
"He was crucial to what we achieved and he goes with the very best wishes of everyone at the club.
"I would like to assure our fans that there is a huge amount of work going on behind the scenes. Our aim is to build a competitive squad for the new season and this deal will give us further ability to strengthen the side.''