Power became head of Westpac's private wealth and insurance division after he decided not to stand for re-election in November 2011.
Walsh spent nine years with accounting firm KPMG's audit and assurance divisions, was chief operating officer for Rugby NZ 2011 and is head of NZ for Cricket World Cup 2015.
"Therese has a strong financial background. In addition, her management and operating experience in large scale projects ... will be particularly useful in the context of governance of NZX's operating businesses," Harmos said.
"Coming from a non-financial markets background, Therese's skill set will enhance the experience and diversity of thought around our board and we are very enthusiastic about her appointment."
Harmos also paid tribute to Moller: "His common sense and straight talking has been a real asset."
NZX shares are up 1 cent at $1.13. The shares peaked at $1.37 in last June following its return of capital to shareholders in May and sank as low as $1.02 in August after poor operating metrics were announced before starting to recover.