Sturridge has signed a long-term contract with Liverpool after passing a medical and will be at Anfield for Wednesday night's game against Sunderland, though his signing came too late for him to be part of the squad.
The 23-year-old England international joined Chelsea from Manchester City for £3.5 million in July 2009 and scored 24 times in 96 appearances for the London club.
"I am humbled and happy to be here," said Sturridge on his arrival at Liverpool.
"Brendan Rodgers said he sees me here for a long time - and I also see myself here for a long time. I've not signed here to play for a couple of years and then move on.
"I've signed to be here for as long as possible. It's a humongous club - for me, one of the biggest in the world - and to have the fans and world-class players we have here is amazing."
Sturridge enjoyed a prolonged run of good form under Andre-Villas Boas at Chelsea last season but subsequently struggled to win a place in the side under Roberto Di Matteo.
In total he started 37 times for Chelsea last season, scoring 13 goals, but this season made only two starts, forcing him to reconsider his future.
With Demba Ba looking set to move to Stamford Bridge after Chelsea matched his £7.5 million release clause earlier on Wednesday, Sturridge has chosen to move to Liverpool to help ease Rodgers's problems in attack.
Liverpool loaned Andy Carroll to West Ham on the final day of the summer transfer window but failed to bring in a replacement, with prime target Clint Dempsey signing for Tottenham.
Now Sturridge, who came through the ranks at Manchester City, arrives as competition for top scorer Luis Suarez, though his versatility means he could also be used to relieve the burden on teenager Raheem Sterling.