The 23-year-old striker had a medical at Melwood last week and completed the formalities on a long-term contract earlier on Wednesday.
Liverpool manager Brendan Rodgers had made Sturridge his priority signing for January, and will be delighted to get the deal done so quickly.
"I am humbled and happy to be here," said Sturridge.
"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 will wear the number 15 shirt at Liverpool, the club have confirmed.