Pressure has been mounting since Henry insulted Governor-General Sir Anand Satyanand last Monday, which caused a diplomatic row.
Last week's incident followed previous derogatory comments he made about an Indian minister.
Henry, who won the People's Choice award at the Qantas Television Awards just three weeks ago, expressed shock about the impact of his actions and sadness it had led to his resignation.
"I am astonished and dismayed that my comments have created a diplomatic incident.
"My style is conversational and of course unscripted.
"I walk the finest of lines and accept that I have inadvertently crossed it from time to time. But I recognise the realities of the situation."
Speculation is rife that TVNZ has agreed to pay six months' salary to Henry, believed to be about $150,000.
TVNZ spokeswoman Megan Richards said any financial settlement was a private matter for Henry.
She said "neither his salary or any financial sorting out is taxpayer dollars".
Last night, Paul Holmes replaced Henry as host of This is Your Life, which featured Mad Butcher Peter Leitch.
Prime Minister John Key, who is to appear on his usual Breakfast slot today minus Henry, said "this episode has been sad and regrettable".
A spokesman for the Governor-General said he was aware of the resignation but no comment would be made at this time.
TVNZ chief executive Rick Ellis said he commended Henry for his decision following his "inappropriate" comments which he said had damaged New Zealand's international relationships.
"As an organisation committed to the principals of free speech it is our job to steer a course between the some times conflicting demands of freedom of opinion and respect for others.
"This is not always easy.
"However, what is clear as an outcome of this episode is that any suggestion of racism, whether intended or not, is unacceptable.
"We are quite clear about that."
Mr Ellis said that as a result of Henry's comments, reviews were under way into the company's editorial policies and presenter code of conduct, particularly around live broadcasts.
Mr Ellis said thousands of supporters had contacted TVNZ and he knew they would be disappointed with the outcome.
"I have a stack of emails on my desk fully 20cm high."
Media commentator Jim Tully, of Canterbury University, did not believe Henry had stepped aside of his own accord.
"I'm sure that Rick Ellis has finally accepted that their immediate reaction was dreadful ... to many and now they had to go beyond that because [of] political fall-out," he said.
"I'm sure there was a lot of pressure behind the scenes."
But, it was a "a reasonably dignified exit", Mr Tully said, "in the sense that he's resigned rather than being seen to have been sacked".
Mr Tully said Henry could still have a career in radio or a more entertainment-based TV programme.
Maori Party co-leader Dr Pita Sharples said the outcome was honourable.
"Paul clearly recognises his behaviour has been unacceptable and this is an honourable outcome that will enable him to consider a new approach to public commentary.
Asked if he was surprised at the response to the controversy, Mr Key said: "Not entirely. These things some times can get a bit of a life of their own. This one certainly has."
Labour Party leader Phil Goff was one of the first to criticise Henry's remarks as racist but said last night the broadcaster had done the right thing.
