The mega-rich Russian businessman agreed to buy 51% of the Royals from John Madejski in January through Thames Sport Investment, owned by Zingarevich.
A statement released by Reading read: "Reading Football Club are pleased to announce that a 51% acquisition by Thames Sports Investment (owned by Anton Zingarevich) has now been completed, complying with all Premier League and Football League requirements."
It went on: "Four additional directors have been added to the Reading Football Club board chaired by Sir John Madejski, namely Anton Zingarevich, Christopher Samuelson, Andrew Obolensky and chief executive Nigel Howe. Ian Wood-Smith also remains a director.
"The football club and TSI would like to thank both the Premier League and Football League for their assistance, and we now enter another bright new era for our historic club, back in the Barclays Premier League."
It was hoped the deal would have been completed in March but delays meant approval has at last been cleared, exactly six weeks after manager Brian McDermott guided the Berkshire outfit to promotion from the npower Championship.
The delays were understood to be due to Reading's promotion, with both the Football League and subsequently the Premier League keen to ratify the takeover in detail.
The deal formally brings an end to Madejski's 22 years in charge of the club, although he remains as chairman, and opens a new chapter in its history, with top-flight football its starting point.
Speculation has been rife that Zingarevich is set to spend big this summer.
Upgrades to the Academy and training facilities have also been looked into while Zingarevich is keen to increase the capacity of the club's stadium should they survive among England's elite.