Adrian, 32, will be an understudy to the European champions’ first choice ‘keeper Alisson.
The Spaniard has previous experience in the Premier League having played more than 100 times for West Ham in the past six years.
“I’m very ambitious, I come here to try to win everything, to try to push Ali from the first minute and to make us better,” Adrian told the Liverpool website.
“We have many competitions ahead – we’re going to fight for it and try to get them.
“I’m looking forward to playing my first game at Anfield and to win as many games as we can.”
Mignolet, capped 22 times by his country, had earlier signed a five-year-deal after passing his medical costing Brugge a reported £6.4 million (7 million euros).
“It’s official, Simon is a Bruges boy!” the Belgian top flight club said on its website, alongside a video of Mignolet arriving at his new home.
Mignolet, 31, for his part tweeted a fulsome farewell to Liverpool.
“It’s been a great ride,” Mignolet said.
“There have been ups, downs and everything in between, but I’ll always look on my time at Anfield with fondness.
“I have no regrets. I’ve given my all and I’ve always done my best to wear the shirt with pride, and to represent the club with dignity and professionalism.
“Once part of the family, always part of the family. Deep inside I’ll always be a Red.”
Liverpool won the Champions League last season but the Belgium international hardly figured as the English outfit conquered Europe for the sixth time and finished just a point behind Premier League champions Manchester City.
Mignolet played for Liverpool on more than 200 occasions after arriving from Sunderland in 2013.
