Worldwide, a total of 305,030 Minis were purchased last year - up 1.2% on the 2012 figure which had also been a record.
Produced in Oxford by BMW, the Mini's biggest market last year was the US where more than 66,000 were bought. The UK was the next-biggest market, with sales of 53,507.
BMW also announced sales of Rolls-Royce vehicles - manufactured at its Goodwood plant in West Sussex -totalled 3630 worldwide in 2013, up 1.5% on the previous record year of 2012.
Sales of BMW cars were also at an all-time high in 2013, with more than 1.65 million bought worldwide - a 7.5% rise on the 2012 total.
Year-end sales were boosted by a record December for BMW cars, with 155,835 sold, as well as 23% hike in BMW 3 Series sales over the whole of last year.
Taking BMW motorcycle sales into account, the BMW group, including Mini and Rolls-Royce, had a record year, with more than 1.96 million vehicles sold globally - a 6.4% rise on the 2012 total.
Welcoming the figures, BMW sales and marketing chief Ian Robertson said: "Despite the prevailing headwinds in many markets, we aim to increase sales and make 2014 another record year."
The BMW statistics were announced a day after Jaguar Land Rover reported record-breaking global sales for 2013 of 425,006 vehicles - up 19% on 2012.