Lomu, who scored 37 tries in 63 matches for New Zealand between 1994 and 2002, had been diagnosed with a rare and serious kidney condition by 1996.
It forced him to quit the game and he had a kidney transplant in 2004, but the organ stopped functioning in 2011.
"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."
Family spokesman John Mayhew told New Zealand television that Lomu's death was "totally unexpected" and that he had only arrived back from the UK on Tuesday, after spending time there for the Rugby World Cup.
New Zealand Prime Minister John Key said: "The thoughts of the entire country are with his family."
Speaking to the BBC, New Zealand Sports Minister Jonathan Coleman said Lomu "was the first global rugby superstar".
He was a "huge inspiration to Polynesian men and actually in later years with his battles against kidney disease, very inspirational to people suffering from chronic diseases as well", he said.
Lomu is survived by his wife Nadene and two sons.
Jonah Lomu scored 43 All Blacks tries, including four against England in the 1995 World Cup semi-final
The son of Tongan immigrants, Lomu made his Test debut in 1994 against France in Christchurch.
As well as playing for several domestic teams in his homeland, he made 10 appearances for Cardiff Blues in Wales between 2005 and 2006, shortly before his retirement.
Despite never winning the World Cup, he is the joint top try-scorer in its history - alongside South Africa wing Bryan Habana, scoring 15 tries in 11 games.
He was at his best at the 1995 and 1999 World Cups, terrifying defensive lines with his speed and size - 192 cm tall (6 feet 4 inches) and weighing about 119 kilograms (18 stone 10 pounds).
In a memorable match against England in the 1995 semi-final, he bulldozed several players and ran straight over the top of full-back Mike Catt on his way to a try.
His performance in that tournament has been widely credited with helping attract the major commercial deals that enabled the sport to enter the professional era.
But a rare kidney condition, nephrotic syndrome, hampered his career. A later transplant was rejected by his body in 2011.
After news of his death broke, former New Zealand captain Sean Fitzpatrick tweeted: "Our thoughts are with the Jonah Lomu family tonight. A very special person."
All Blacks World Cup winner Dan Carter tweeted: "I still can't believe the sad news. Love and thoughts go out to Jonah's family."
And former Wales fly-half Jonathan Davies said: "Can't believe that Jonah Lomu has passed away. Was with him and his wife and family for an evening last month.
"So sad, life is so cruel. RIP Jonah you were a true legend and a gentleman. You changed the game of rugby and will be sorely missed. My thoughts are with your family."