Lomu, who scored 43 tries in 73 matches for New Zealand between 1994 and 2002, had been diagnosed with a rare and serious kidney condition.
It forced him to quit the game and he had a kidney transplant in 2004, but the organ stopped functioning in 2011.
He is survived by his wife Nadene and two sons.
"Jonah was a legend of our game and loved by his many fans both here and around the world," said New Zealand Rugby chief executive Steve Tew.
"We're lost for words and our heartfelt sympathies go out to Jonah's family."
Lomu made his Test debut in 1994 against France in Christchurch.
Despite never winning the World Cup, he is the joint top try-scorer in its history - alongside South Africa wing Bryan Habana - with 15 tries in 11 games during the 1995 and 1999 tournaments.