Hart, who coached the all-conquering Auckland provincial side in the 1980s, had a lengthy commercial career before he took over as All Blacks coach in 1996 shortly after the game went professional.
He resigned after the All Blacks were knocked out by France in the semi-finals of the 1999 Rugby World Cup.
Former Cabinet Minister Sam Lotu-Iiga was also appointed to the Blues board along with NZR board member Richard Dellabarca.
"We are pleased that John, Richard and Sam are available to represent NZR's partnership interest in the Blues Super Rugby club," NZR chief executive Steve Tew said in a statement.
"In combination with other recent changes to the coaching team and re-signing and recruitment of key players, this is one of many steps to help rebuild the success of the club."
The Blues, Super Rugby champions in 1996, 1997 and 2003, have been the worst-performing New Zealand side in the competition since 2013.
They have failed to make the playoffs in each of the years since and finished ninth in a reduced competition of 15 teams this year with seven wins.
NZR sold ownership of the management licences of their five Super Rugby franchises from 2013, with the sale split between the team's component provincial unions and private investors Bolton Equities Limited (BEL).
The national governing body bought back BEL's stake last month.
(Reporting by Greg Stutchbury; Editing by Nick Mulvenney)
