Rolls-Royce chairman and BMW executive Ian Robertson told the BBC the firm is "resolving the situation quickly".
The German firm said the recall was due to a fault with the power-braking system but the cars were not unsafe.
The recall affects V8 and V12-powered BMW 5 Series, 6 Series, 7 Series, and Rolls-Royce models produced between July 2001 and November 2009.
Of the total, 11,427 cars - including 905 Rolls-Royces - are in the UK, and 198,000 in the US.
BBC News - BMW car recall being resolved 'quickly' executive says
Oh dear, at least it takes the heat off the Japanese for a while
