"We have purchased the club with no debt on the club," said Gillett. "We believe in the future of the club, the future of the league, the new TV contracts are outstanding and we are proud to be a part of it.
"This is truly the largest sport in the world, the most important sport in the world, and this is the most important club in the most important sport in the world.
"What a privilege we have to be associated with it and we hope that with the good graces of Rick and his team that we will have on-the-pitch success and economic success."
They said the club would consider selling the naming rights to the new stadium.
Gillett added: "If the naming rights are worth one great player a year in transfer spending, we will certainly look at that as a serious option."
But both Gillett and Hicks vowed to safeguard the legacy of the club and leave Parry and manager Rafa Benitez to do their jobs.
A club statement earlier confirmed that a deal had finally been done after a three-year search for new owners.
It said: "Liverpool FC today announced that the board have agreed the terms of an offer for the club from Mr George Gillett and Mr Tom Hicks.
Existing chief executive Rick Parry will be left to run the club
"The board are unanimously recommending that the club's shareholders accept this offer."
Moores was not present at the official announcement, with Parry saying it was probably "the worst day of his life" and the "biggest decision".
But in a statement he said: "This club is my passion and forms a huge part of my life. After much careful consideration, I have agreed to sell my shares to assist in securing the investment needed for the new stadium and for the playing squad.
"I urge all my fellow shareholders to do the same and to support the offer. By doing so, I believe you will be backing the successful future of Liverpool.
"I am also delighted to accept the offer from the Hicks and Gillett families to continue my involvement in the club by becoming honorary life president."
Parry added: "This is great for Liverpool, our supporters and the shareholders - it is the beginning of a new era for the club.
Hicks, who owns the Dallas Stars ice hockey club as well as the Texas Rangers baseball team, joined forces with Gillett to gazump rival bidders DIC last week. "They are bringing to the table tremendous and relevant experience, a passion for sport, real resources and a strong commitment to the traditions of Liverpool.
"We know that George and Tom want a long-term relationship with Liverpool and that they also understand the importance of investing in our success both on and off the field.
"They have made clear their intention to move as quickly as practicable on the financing and construction of our proposed new stadium at Stanley Park and also to support investment in the playing squad."
Both Parry and Gillett said the addition of Hicks last month had been crucial in sealing the deal.
The Hicks family and the Gillett family are extremely excited about continuing the club's legacy and tradition
Joint statement from Hicks and Gillett
But Gillett dismissed reports that said he had planned to groundshare with neighbours Everton, saying that Parry had warned him off such a suggestion at their first meeting.
Gillett, owner of Montreal Canadiens, has impressed Liverpool with his proposals and the speed at which he completed due diligence - the process of investigation by potential investors - in three days.
The 68-year-old American has also stressed his experience in running successful sporting operations.
It is thought to be the first time that two owners of rival sports clubs in one league have combined to purchase a club in another.
Liverpool will become the third Premiership side to come under the control of American owners, following the takeovers of Manchester United and Aston Villa in recent years.
A joint statement from Gillett and Hicks said: "Liverpool is a fantastic club with a remarkable history and a passionate fanbase.
"We fully acknowledge and appreciate the unique heritage and rich history of Liverpool and intend to respect this heritage in the future.
"The Hicks family and the Gillett family are extremely excited about continuing the club's legacy and tradition.
"We are particularly pleased that David Moores and Rick Parry will have a continuing involvement in the club. For us continuity and stability are keys to the future."
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