Henry, 61, had until 0400 GMT on Monday to apply for the job after the NZRU rejected a proposal to reappoint his coaching team, which included Steve Hansen and Wayne Smith, after the heavily favoured All Blacks were sensationally knocked out in the World Cup quarter-finals.
"I have applied for the All Blacks coaching position because I believe I can add further value," Henry said in a statement.
"I'm passionate about coaching and this team.
"Obviously the Rugby World Cup was a big disappointment and I am responsible, but I believe we can learn from that experience and develop into an even stronger All Blacks team in the future."
"I have applied for the All Blacks coaching position because I believe I can add further value."
All Blacks coach
The NZRU said seven candidates had applied for the job, but declined to name any applicants due to privacy legislation.
"Once a shortlist of candidates is finalised we intend to ask the applicants to agree to be named, given the strong public interest in both the role and the process," Mike Eagle, NZRU board member, said.
Robbie Deans, Canterbury Crusaders coach, who was also suggested as a candidate for the vacant Australian coaching job, Ian Foster (Waikato Chiefs) and Colin Cooper (Wellington Hurricanes) are all reported to have applied for the position.
Deans has been touted by the New Zealand media as the hot favourite to succeed Henry after winning four Super titles and reaching two other finals and a semi-final in his eight years in charge of the Christchurch-based franchise.
Cup failure overshadows excellent record
Henry's deputies Smith and Hansen both said they would be happy to work with him again as a panel.
"Graham has my full support. I believe that we three coaches have worked well together over the last four years," said Hansen.
"We have learned a lot... (and) we'd like the opportunity to use that knowledge to improve the team further."
New Zealand won 42 of 48 matches under Henry, taking the Tri-Nations title in 2005, 2006 and 2007, completing a series whitewash against the British and Irish Lions and a grand slam over England, Scotland, Wales and Ireland.
They went into this year's World Cup as overwhelming favourites to win the Webb Ellis Cup but were beaten by hosts France in the quarter-finals.
A decision on the new coach is expected by the end of December.