David Moores, Liverpool chairman, said that the deal was a, "great step forward for [the club's] shareholders and fans".
Gilett and Hicks beat off competition for the club from Dubai International Capital by tabling an offer worth £5,000 a share. DIC's offer was tabled lower at £4,500 a share.
The deal values the club at £174m and, taking into account the club's debt and the possibility of funding a new stadium, could eventually reach an estimated £470m.
Moores said: "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 Football Club."
As part of the deal ITV has followed Moores' advice and disposed of its 9.99% shareholding in the club at a price of £5,000 per share.
The deal will put £17.4m back into the ITV coffers, and is part of the broadcaster's disposal of £500m worth of non-core assets. ITV still owns a 5% stake in Arsenal worth an estimated £30m.
Gillett, who has an estimated fortune of $860m (£437m), began his career in the broadcast industry before moving into the meat business, and is the owner of sports and entertainment promotion business Gillett Entertainment Group. He owns Canadian ice hockey team Montreal Canadiens and once also owned a stake in the Harlem Globetrotters.
Hicks is the multi-millionaire owner of Dallas Stars ice hockey team and the Texas Rangers baseball team.
Liverpool FC has long sought a takeover in order to continue competing with Premiership rivals Chelsea FC, which was bought by Russian oil billionaire Roman Abramovich for £140m in 2003, and Manchester United, which was controversially acquired by US sports tycoon Malcolm Glazer for £790m in 2005.