Owner Geoff Sewell has retired and the purchase price has not been revealed.
Last year, the dealership – now rebranded Elms Stansted – sold nearly 700 new and 470 used BMWs, and 250 new and 120 used Minis.
The group’s other BMW sites are in Bedford and Cambridge, each with a turnover of £34m. It also holds the Mini franchise, and trades as Elms.
The acquisition takes BMH’s annual turnover to £120m, which includes sales at its ChryslerJeep Dodge and Saab authorized repairer sites in Bedford.
John Thompson, BMH managing director, says: “We have held the franchise since 1990, and made known to BMW our wish to expand.
“We have trebled in turnover in three years, and this purchase further consolidates our position as one of the UK’s most rapidly growing, privately owned motor retail groups.
“We are an acquisitive group and the purchase of Sewell fits in perfectly with our long-term plans.”
BMH is part of Bedfordia Group plc, which also owns businesses in property, agriculture and eco-technology. Bedfordia Motor Holdings, which employs 270 people, says it now sells an annual 2,500 new and 1,800 used BMW and Mini models.
The Cambridge businesses were acquired in 2003, and the group has aftersales facilities in the East Midlands and East Anglia.
BMH began as a used 4x4 centre in the village of Milton Ernest, near Bedford, in 1981.