Brazilian playmaker Lucas Moura has extended his contract with French champions Paris Saint-Germain until 2019.
Burnley's new sporting director Frank McParland hopes to be able to start next season alongside Sean Dyche.
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.''
Simon Mignolet factfile
1988: March 6 - Born in St. Truiden, Belgium.
2004: Signs for local club St. Truiden.
2006: Breaks into the St. Truiden first team at the age of 18.
2009: April 11 - Gets on the scoresheet with the final goal in a 5-1 away win at Ronse.
April 26 - St. Truiden win a surprise promotion to Belgium's top flight.
2010: Named Belgian goalkeeper of the year after helping St Truiden avoid relegation in their first season in the top flight.
June 17 - Signs for Sunderland for £2million.
August 14 - makes his Sunderland debut in a 2-2 draw against Birmingham at the Stadium of Light.
September 1 - receives his first full international call-up for Belgium having previously represented his country at Under-19 and Under-21 level.
2011: March 25 - makes his Belgium debut, keeping goal in a 2-0 win away to Austria.
October 29 - suffers a broken nose and eye socket in a challenge with Emile Heskey, putting him out of action for two months and forcing him to wear a protective mask on his return.
2012: December 26 - Excels in Sunderland's goal as they beat defending champions Manchester City at the Stadium of Light.
July - achieves a degree in Social Sciences and Politics from the University of Leuven.
2013: January 11 - voted the North East Football Writers' Association's Player of the Year for 2012.
May 15 - Sunderland secure Premier League survival under Paolo Di Canio as Wigan lose at Arsenal.
May 19 - Mignolet keeps goal in Sunderland's final league game at Tottenham, meaning he has been an ever present in the Wearside club's Premier League season.
June 25 - Joins Liverpool on long-term contract.