Peau, who won gold for New Zealand in the superheavyweight division in Edinburgh in 1986, recently underwent brain surgery.
Born in Samoa as Ti'a James Senio Peau, he grew up in Auckland.
After his Commonwealth Games success as an amateur, which also included the Australian heavyweight title, Peau turned professional in 1988 and fought under the name Jimmy Thunder.
Peau won two world heavyweight belts during his career - the WBF in 1993 and IBO in 1994.
He was famous for knocking out American Crawford Grimsley with his first punch in 1997.
The fight, lasting 1.5 seconds before the count, is a record for the world's fastest knockout.
His last bout was in 2002.
In total, Peau had 49 professional fights that included 35 wins (28 by knockout) and 14 losses.
Boxing commentator Mike Angove said Peau was one of the trailblazers of boxing in New Zealand.
Angove said he had tremendous highs and a number of lows and felt that if he had been managed better he could have gone a lot further.
Peau was reported to have lived rough in the United States for a while when his boxing career ended.