The former Walt Disney chief executive entered negotiations over purchasing the club earlier this year, and the £5.67m deal for 100% ownership has now been officially confirmed.
Eisner will invest an extra £10m in addition to the takeover fee, while his three sons Breck, Eric and Anders have been appointed to the Portsmouth board.
"My family and I are thrilled to take on this incredible responsibility as stewards of a football club with such a rich heritage," Eisner told the club's official website.
"We have come to know the Pompey community in recent months and we are extremely impressed by their passion, dedication and love for their club."
Portsmouth CEO Mark Catlin added: "We have been on a remarkable journey and one that everyone associated with this amazing club should rightly be proud of. It has been an honour and privilege for me personally to represent Pompey and our incredible fans during this time.
"Now we embark on an exciting new chapter in the club's history and one that, under the stewardship of Michael Eisner, his family, Andy Redman and the Tornante group, I am totally confident will continue to build on the strong foundations that have been built over the past four seasons."
Portsmouth was previously shared between the Pompey Supporters Trust and 16 other 'presidents'.