Westover chairman Peter Wood said all staff at the outlets in Poole, Christchurch and Ferndown would be retained and integrated into Westover.
It is the first time Westover has represented Peugeot. The group now has 21 outlets and 600 staff.
The acquisition is expected to push Westover up into the 40s from its current 54 ranking in the latest AM100 with £175 million turnover.
Andrew Hartwell, managing director of George Hartwell, said: "We were anxious to ensure continuity, so we’re delighted that our staff are secure and that our customers will benefit from Westover’s first rate service.
"The sale made good economic sense for us, but it also means that local Peugeot drivers will see improved provision in the long term, thanks to Westover’s size and its commitment to the region."