The ruling at London's High Court came less than two hours before the concert in the capital's Royal Albert Hall was due to begin.
"We are over the moon that Busta Rhymes will be able to play the Orange Rockcorps show tonight as planned in front of 5,000 young people who have volunteered four hours of their time to community projects," said a spokeswoman for organizers Rockcorps.
Officials at London City Airport detained the 36-year-old rapper after he arrived early on Thursday, citing "unresolved convictions in the USA."
They tried to put Rhymes on a flight to Amsterdam but his lawyer obtained an injunction and applied for a judicial review of the decision not to grant him admission.
This year Rhymes was sentenced to three years' probation for beating a fan who spat on his car in August 2006 and assaulting his driver that December.
The London show, which will feature British bands The Automatic, Feeder and U.S. soul singer John Legend, is being held for 5,000 fans who clocked up a total of 20,000 hours of voluntary work.
Britain's Home Office said on Thursday that previous criminal convictions and a person's character and conduct were assessed before an individual was allowed into the country.
(Reporting by Mike Collett-White)
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