The rare Tyrannosaurus bataar, 7m long (23ft), was bought by an anonymous bidder for more than $1m (Â£630,000) in New York.
The sale went ahead despite protests from the Mongolian president.
Elbegdorj Tsakhia says the skeleton, unearthed in the Gobi Desert, came from Mongolia and that exporting fossils found in the country is illegal.
The auctioneers, Heritage Auctions, say the specimen was imported legally. A restraining court order in the name of the Mongolian leader was put on the sale.
Tyrannosaurus bataar is an Asian cousin of the meat-eating Tyrannosaurus rex.
The skeleton in New York is thought to be one of the most complete and well preserved ever discovered, says the BBC's Jonathan Blake in Washington.
"When it comes to dinosaurs, number one, dinosaurs in general are extremely rare. But the rarest of the dinosaurs are the carnivores, the meat eaters - the top of the food chain if you will," David Herskowitz, director of natural history at Heritage Auctions, told APTV.
"And, of all the meat eaters that are out there, the most famous are the Tyrannosaurids. They are the most desirable, but they are the most elusive. They are the most difficult to find. Even though they are so big, there are not that many of them around."
Found about seven years ago in the Gobi Desert, the T. bataar remained in storage in England.
The T. bataar was slightly smaller and had longer arms than its cousin, Mr Herskowitz said.
This is the second Tyrannosaurid to be sold at auction, says Mr Herskowitz. The first was a T. rex named Sue sold in 1997 for more than $8m.
Lawyers for the auction house say the sale did not break any US laws - but it will not be confirmed until it has been approved by a US court.

Bristol Sport Ltd, which owns the football club, wants to replace two stands to increase capacity.
The plan is an alternative to proposals to build a new stadium at nearby Ashton Vale, which has been delayed by an application for a town green.
Majority shareholder Steve Lansdown confirmed the club would begin work at a shareholder meeting on Tuesday.
The work was approved by Bristol City Council in November.
Mr Lansdown told the club's official website: "We'll sign the section 106 agreement any day now, and then we have six weeks to wait for the judicial review period.
"We wanted to give some certainty to supporters, so if we get through to March with no judicial review, then we will be going ahead with the redevelopment plans, starting in May."

The song topped the UK singles charts in February 1969 and remained number one for four weeks.
It was also number one in many other countries and won the Ivor Novello award for best song composition.
He died peacefully after a six-year battle with Progressive Supranuclear Palsy, a family statement said.
The statement said his closest family were "with him to the last" and that many people would miss his songs and his music.
Where Do You Go To (My Lovely), a song about a girl born in poverty who becomes a member of the European jet-set, was replaced as number one by Marvin Gaye's I Heard it Through the Grapevine.
It was included in the compilation programme One-Hit Wonders at the BBC, which was broadcast on BBC Four last year, although Sarstedt also reached number 10 in the charts with Frozen Orange Juice in June 1969.
He wrote more than a dozen albums in a career that spanned more than 50 years, releasing his last, Restless Heart, in 2013
Born into a musical family in India, Sarstedt was one of three brothers who all enjoyed success in the UK singles chart.
His older sibling, Richard Sarstedt, who performed under the stage name Eden Kane, also topped the charts with Well I ask You in 1961, while younger brother Clive, performing under the name Robin Sarstedt, reached number three in 1976 with My Resistance is Low.
Sarstedt's music reached new audiences when Where Do You Go To (My Lovely) was included in the Wes Anderson films Hotel Chevalier and The Darjeeling Limited, which were both released in 2007.
According to his website, he retired in 2010 because of his illness - a rare, progressive neurological condition.
A row has broken out over the sale of a dinosaur skeleton at auction in the US.
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A £40m revamp of Bristol City's Ashton Gate ground will go ahead this summer, the club has announced.
[NEXT_CONCEPT]
Singer-songwriter Peter Sarstedt, best known for the song Where Do You Go To (My Lovely), has died at the age of 75, his family has said.