The 32-year-old Spaniard left West Ham after six years this summer and was due to have talks with Real Valladolid with a view to joining them before receiving an offer from the European champions.
A move is expected to be completed soon given that Liverpool kick off the new Premier League season, and the club would like to have an experienced No. 2 in position at Anfield.
Mignolet signed for Belgian side Club Brugge on Monday in a deal worth up to £8 million for the Reds.
The 31-year-old, who was part of the squad in the Community Shield defeat to Manchester City on penalties, said his goodbyes to his team-mates before boarding a private plane from London to Belgium.
The fee is an initial £6.4 million, rising to £8m with achievable add-ons.
Jurgen Klopp had hoped to keep the Belgium international, but Liverpool always maintained that if there was a good deal on the table that would benefit Mignolet, they would consider it, as was the case when Lucas left for Lazio.
He made 204 appearances for the club and departs on excellent terms having been a superb professional during his six-year spell on Merseyside.