Mr McMahon, who sold Audi dealer Lomond Motors to Lookers for £15 million in 2012, has bought the property and assets from Murray Motor Group in Edinburgh.
That includes a showroom at Sighthill in the capital as well as the right to represent Rolls Royce across Scotland and Northern Ireland as well as Aston Martin in Scotland.
Current turnover is put at around £20 million, with Mr McMahon intending to grow that towards £30 million.
He said: "When I sold Lomond I always knew I would come back in. It was just a case of finding the right opportunity. This was particularly appealing because of the brands and the scale. We felt it was something we could really shape and turn into something quite special.
"We always thought Audi would be a tough act to follow, and it is, but this takes us into a sector of the market we have never really operated in before."
Mr McMahon, who started in the industry as a technician at 16, said he was excited at the prospects both car brands offer, citing the expectation of a number of new models arriving into the market. Another plan to expand the scope of the business is in the second-hand market with a focus on luxury and sports cars.
The 56-year-old suggested he would have been keen to snap up the brands even if the economy had not been showing its signs of recent improvement.
He said: "Having said that, I think it is a particularly good time, with the development and capital the brands are putting in as well as the upturn in the economy with people feeling that little bit more confident."
Mr McMahon's son Chris becomes operations director with Brian Ritchie installed as finance director.
A further three staff have been added to the existing workforce of 15 and Mr McMahon said further hires are planned while options for an additional physical site are also being mulled.
He said: "There is the possibility we may do something in another location to get better coverage, but more of a satellite type dealership."
The deal was funded by the Scottish corporate banking team at Barclays.
Alan Maudsley, from Barclays, said: "Our team has worked with Hugh in his previous businesses and his wealth of experience in the motor industry coupled with his robust plans for growth meant we had the appetite to support this deal.
"Car sales have long been a measure of economic confidence and although the luxury end of the market has been affected less than most, it too is starting to see an upturn in sales making the business an attractive investment choice."
Lomond had a workforce of around 350 and dealerships in Ayr, Edinburgh, Glasgow and Stirling when Mr McMahon sold it.