Milner will join the Merseyside outfit next month when his current contract with Premier League rivals City runs out.
The England international midfielder won two Premier League titles, an FA Cup and the League Cup during his five years at City.
City centre-back Kompany has taken to Twitter to wish Milner well, while praising his “drive and passion” - qualities which will surely please Liverpool fans.
You'll be missed at City brother, as a teammate and a friend! Your drive and passion were inspirational. Good luck! pic.twitter.com/YzqVWlgrJn— Vincent Kompany (@VincentKompany) June 4, 2015
Milner has been on the books of City since 2010, but he has never really been guaranteed a regular place in the starting line-up.
The former Leeds United and Aston Villa star scored five goals and created 52 chances in 32 Premier League appearances in the recently concluded 2014-15 campaign, while having a pass accuracy of 79% and a shot accuracy of 41%.
The Englishman is not one of the most technically gifted footballers, but he is an all-round midfield player who works hard and does what he is told.