The Reds have been pursuing the 23-year-old England international for some time, having first expressed their interest in him back in August, and are believed to have paid in the region of £12million.
"I am humbled and happy to be here," Sturridge told Liverpool's official website. "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 began his career at Manchester City where, having been top scorer in the 2008 FA Youth Cup triumph, he scored six goals in 32 appearances - although the majority of those were as substitute.
He moved to Stamford Bridge in the summer of 2009 where his record improved to 24 goals in 96 games, although he made only 31 Premier League starts in three and a half years.
During that time he also had a five-month spell at Bolton, scoring eight goals in 12 matches.
At the start of this season he expressed his desire to leave, especially as he has ambitions to improve his chances in the England squad having made his full international debut in November 2011 and represented Great Britain at the Olympics.
Rodgers initially tried to bring Sturridge to Anfield on loan in August but the player wanted a permanent move.
In the intervening period Rodgers has been left low on options in attack, with Andy Carroll's loan to West Ham and Fabio Borini's broken foot leaving Luis Suarez as his only fit striker.
"I'm hugely excited. I just can't wait for the games to start rolling on," added Sturridge. "I've not played for a while - I've had a couple of injuries over the last few months - but I'm just happy now to join such a great club, to be part of a revolution and to be part of something new and something special.
"Hopefully we'll be able to bring a bit of success for the fans.
"I see myself as a striker. I think I perform best there because my attributes, I believe, are best as a central striker.
"But I have played on the wing and have learned a lot doing so. I'd never refuse to play in that position and I've never demanded to play up front, either.
"For me, whatever the manager wants me to do I will do it and work as hard as I can for the club and the fans."
Sturridge is relishing the prospect of linking up with Suarez in particular.
"To have him as a team-mate is great," he said. "He's a very good player, very talented and rated as a one of the best players in attacking positions in the world right now.
"It's good to be part of a team with him in and I'm sure we'll be able to play well together.
"With Luis, Raheem (Sterling) and the other players that are here, it's going to be great for myself and I'm sure we'll connect well together.
"We all have similar attributes so hopefully we'll be able to create a few nightmares for defenders."