The $476 million deal with New England Sports Ventures ends the turbulent three-year ownership by Tom Hicks and George Gillett Jr.
The sale went through after Hicks and Gillett withdrew the temporary restraining order they had obtained in a Texas court. Later, they also dropped their claim for $1.6 billion in damages.
The deal came on the day the Royal Bank of Scotland and Wells Fargo had set as the deadline for repayment of the club's debts, which have risen to more than $456 million.
"We are committed first and foremost to winning," said John Henry, the financier who heads NESV. "We have a history of winning, and today we want LFC supporters to know that this approach is what we intend to bring to this great club."
Amid the takeover turmoil, Liverpool is mired in the relegation zone after its worst start to a league season since 1953.
"As every Liverpool fan knows, the most nerve-racking way to win a match is by a penalty shootout," club chairman Martin Broughton said. "But in the end, as long as you get the right result, it's worth the wait. We've got the right result."
Broughton said the deal "comprehensively resolves the pressing issue of the club's debt and should give staff, players and fans great confidence regarding the future of Liverpool FC."
Liverpool went to the High Court in London twice this week to win approval for the sale over the objections of Hicks and Gillett, who claim the price undervalues the 18-time English champions.
"It's been pretty stressful, but we've been confident all the way through that we'd get there," Broughton said outside the London law offices where the deal was signed.
Hicks and Gillett originally said that even though they were withdrawing the restraining order, they would pursue a claim for $1.6 billion in damages. However, later in the day their attorney said they were dropping the claim to comply with an English court order.
But they suggested the fight isn't over, saying, "We believe that once the English court finally has a chance to hear all the facts a very different picture will be painted."
Broughton said he would stay as chairman in a transitional role, while Henry decides how he wants to run the club.
Henry reached out to Liverpool fans in a bid to break with the deeply unpopular Hicks and Gillett.
"We're not going to have a lot to say," he said. "We are going to do a lot of listening. We have a lot to learn. Our actions will hopefully speak for words."
Henry said it was too early to decide on specific plans, but noted the Red Sox are the second-highest spending club in baseball. Liverpool, under manager Roy Hodgson, is hoping to sign new players in the next transfer period in January.
"We are here to win," Henry said.
Henry wouldn't say whether NESV would build a new stadium for Liverpool or refurbish its existing one at Anfield.
Liverpool plays city rival Everton on Sunday at Goodison Park. Henry indicated he won't attend, saying "I think it's better for our first experience with the supporters to be at home."
Liverpool's next home game is against Blackburn on Oct. 24.
NESV was represented in the deal by Inner Circle Sports, a New York-based financial company.
Hicks and Gillett called the takeover was "illegal" and an "extraordinary swindle." Hicks said Royal Bank of Scotland refused to allow him to repay Liverpool's debts to prevent the sale.
"This was a conspiracy of the British establishment Royal Bank of Scotland, our chairman (Broughton) and our highly compensated employees," Hicks told The Associated Press.
RBS was partly nationalized in 2008, with the British government taking an 84 percent stake after it was brought to the brink of collapse by the global economic crisis.
"This outcome not only devalues the club but it also will result in long-term uncertainty for the fans, players and everyone who loves this sport because all legal recourses will be pursued," said Steve Stodghill, the Texas attorney representing Hicks and Gillett. "Mr. Hicks and Mr. Gillett pledged to pay the debt to RBS so that the club could avoid administration that was threatened by RBS. That offer was rejected.
"It is a tragic development that others will claim as a victory. This means it won't be resolved the way it should be resolved. My clients worked tirelessly to resolve these issues but RBS would not listen to any reasonable solution and the directors acted selfishly and illegally."