The US motor giant adds the Rover name to the other British motoring marques it already owns in Land Rover, Jaguar and Aston Martin, which form Ford's Premier Automotive Group in the UK.
Ford says it had been in talks with BMW for several months after retaining first refusal to buy the Rover brand name when it acquired Land Rover in 2000.
The MG Rover car company collapsed in early 2005 after a deal with Shanghai Automotive collapsed. That deal finished the company, which had been bought from BMW for a symbolic £10 by former Rover directors, the Phoenix consortium in 2000.
Having pulled out of the deal to buy MG Rover, Shanghai Automotive still holds the rights to the Rover 25 and 75 models and it is talking about restarting production in the UK next year.
The MG Rover company was bought by another Chinese firm Nanjing Automobile, which plans to make MG sport cars at Rover's former Longbridge plant in Birmingham.
BMW is understood to have held talks with Shanghai Automotive and Nanjing Automobile about buying the rights to the name.
Ford is not saying what it plans to do with the Rover brand now it has the rights to the trademark, but it is thought unlikely to bring back any Rover saloon models.
Instead, it is believed to be considering plans for new models associated with the Land Rover brand because of the close link in people's minds between Rover and Land Rover.
A spokesman for Ford said: "It is in the interest of the Land Rover business to do this. We're not ready to say what we plan to do with the Rover name.
"We believed then [in 2000], as we do now, that it is in the interests of the Land Rover business to own the Rover trademark."
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