The former Impact and Toronto FC defender served as Montreal's manager from 2011 to 2013.
He replaced Matt Jordan, who left on Nov. 4 to become vice-president and general manager of the Houston Dynamo.
Braz will manage the team's salary cap and act as a liaison between the club and Major League Soccer. He will work with manager Frank Klopas on contract negotiations and strategy and will handle day-to-day operations of the MLS squad.
He will report to executive vice-president of soccer operations Richard Legendre.
The 33-year-old Braz played seven seasons for the Impact. He also played for Toronto FC during its expansion season in 2007 and for Swedish second division club Vasteras in 2003.
The Montreal native also played in 12 games for Canada's national team.