The 25-year-old England international has played just twice since he picked up the injury in the 2-1 loss to Manchester United on 22 March.
"Just want to let the world know I've had a successful operation on my hip and I want to thank God for allowing that to be possible," Sturridge said.
"Onwards and upwards from here. Thanks for the support."
Sturridge scored 24 goals from 33 appearances last season but has been blighted by injuries this term, appearing in only 18 matches.
It is the second time this season he has travelled to the States in an attempt to rectify his fitness problems.
Towards the end of a five-month absence with a thigh problem sustained on international duty in early September - which was then followed by a calf strain - he spent 10 days in Los Angeles as part of his rehabilitation.
The striker has not featured since playing 85 minutes of the FA Cup quarter-final replay at Blackburn on 8 April.
Liverpool manager Brendan Rodgers last week said the club's medical team believed they had made a breakthrough in the diagnosis of Sturridge's injuries, which the player has previously suggested may be hereditary.
"I think we have found some underlying issues that maybe relate to Daniel's problems this season and the ongoing ones he's had," Rodgers said.
Liverpool striker Daniel Sturridge has had "successful" surgery on a hip injury in the United States.