"It is no longer practical in the current environment for me to do the job I was employed to do, and have so enjoyed doing," he said tonight.
"It is also difficult for TVNZ to get on with the business of being a first class broadcaster as long as I remain."
Henry has been the subject of several hundred complaints to the broadcaster over racist remarks he made about Governor General Sir Anand Satyanand and his mocking of the name of Delhi Chief minister Sheila Dikshit.
TVNZ chief executive Rick Ellis said he had met Henry today and accepted his resignation.
"In doing so, I offer my sincere apology on behalf of myself and TVNZ, to all those who have been offended by Paul's inappropriate on-air comments," he said.
"I will be apologising in person to the Governor General. I also apologise to the Indian community, both here and in India."
