The Court of Arbitration for Sport (Cas) announced the club were cleared of “disguising equity funds as sponsorship contributions”.
Uefa issued the ban in February after ruling City had committed “serious breaches” of Financial Fair Play regulations between 2012 and 2016.
City’s fine has been cut from 30m euros (£26.9m) to 10m euros.
In delivering the ruling on Monday, Cas said City did “fail to cooperate with Uefa authorities” but overturned the decision by Uefa’s club financial control body (CFCB) to ban them.
City said the decision was “validation of the club’s position and the body of evidence that it was able to present”.
“The club wishes to thank the panel members for their diligence and the due process that they administered,” City added.
What did the ruling say?
Cas’ ruling means City, who are guaranteed to finish second in the Premier League this season, will play in the 2020-21 Champions League.
In this year’s competition, Pep Guardiola’s side face Real Madrid in their last-16 second leg at Etihad Stadium on 7 August. They lead 2-1 from the first leg and will face Juventus or Lyon if they progress.
Cas, who will provide full written reasons for the ruling “in a few days” said the decision “emphasised that most of the alleged breaches reported by the adjudicatory chamber of the CFCB were either not established or time-barred”.
It added that in clearing City of the more serious charges surrounding “dishonest concealment” of sponsorship deals it was “not appropriate to impose a ban on participating in Uefa’s club competitions” for the lesser charge of “obstructing the CFCB’s investigations”.
On reducing the fine, Cas said that, while it considered “the importance of the co-operation of clubs in investigations conducted by the CFCB” and Manchester City’s “disregard of such principle and its obstruction of the investigations”, the Cas panel “considered it appropriate to reduce Uefa’s initial fine by two-thirds”.
It added: “The final award with reasons will be published on the Cas website in a few days.”
Uefa said it noted there was “insufficient conclusive evidence to uphold all of the CFCB’s conclusions in this specific case and that many of the alleged breaches were time-barred”.
The governing body added: “Over the last few years, Financial Fair Play has played a significant role in protecting clubs and helping them become financially sustainable and Uefa and the European Club Association remain committed to its principles.”