The deal is the latest move into the sector by RSBG who snapped-up Pell Frischmann in 2015.
McBains Cooper is led by chief executive Michael Thirkettle and specialises in design, architecture, planning, engineering, construction, project management and sustainability.
Thirkettle said: “Today marks an exciting new chapter in the long and proud history of McBains Cooper, as we strengthen our imprint and extend our global reach.
“RSBG only invests in companies that have a future of both expansion and sustainability, that mirror their own values, and we are delighted to join with them in this new enterprise.”
Jürgen Wild, Managing Director of RSBG, said: “McBains Cooper provides a great fit with our investment criteria, a highly-respected property and construction consultancy that has an enviable reputation across all major market sectors.
“They have combined technical excellence with exemplary customer service. Adding dedicated project management capability and a multi-discipline approach is a major step in our strategy to build a fully-fledged consultancy group.
“In the last three years RSBG has significantly invested in built environment consulting businesses. The fourth transaction in this segment underlines our commitment to the UK market.”
RSBG added: “The move will see no changes made to the McBains Cooper management team, nor alter any of the professional or operational personnel.”