Hager, who has led the Black Sticks to gold at the 2018 Commonwealth Games, will start his new role immediately. New Zealand assistant coach Sean Dancer will become acting head coach as the team prepares for the FIH Pro League which starts in just over two weeks.
Hager's departure came during a review into the environment inside the women's team.
The review was launched in September after it emerged that in August Hager mistakenly sent an email bagging players to the entire team. The email was sent during the team's Hockey World Cup campaign and was meant for team management only.
The findings from the review were expected to be released in November, but now won't be announced until the end of this month.
Hockey New Zealand acting board chair Shane Collins emphasised that Hager was leaving on his own terms.
"We are extremely disappointed to lose one of the world's top coaches. Mark and his coaching staff have continued to have the support of the Board and management and we wish him well in his next endeavour. His legacy will take some matching," says Collins.
The 54-year-old Australian had been the Black Sticks' coach for eight years and was contracted through to 2020.
The email Hager sent appeared to cause a split inside the team, with some players offended by it, but seven former Black Sticks women's players went public in support of the coach.
Katie Glynn, Laura Douglas, Lucy Talbot, Anna Alexander (Thorpe), Bianca Russell, Emily Gaddum (Naylor) and Krystal Forgesson sent a letter backing Hager, rejecting allegations of a negative environment within the Black Sticks programme.
Hager, a former Australian international, said it is sad to leave a team that he regards as his whanau.
"I've been fortunate to coach the Black Sticks for a decade and even more fortunate to have two world-class players in Kayla Sharland and Stacey Michelsen as my captains to help us achieve goals that were firsts for this team."
He had been especially looking forward to leading the group through to the Tokyo Olympics.
"The team has the potential to succeed in Tokyo and I wish them well. I have been torn over the last six months, firstly whether to apply for the England/Great Britain role and then whether to accept it. But given its profile as one of the pinnacle coaching roles in world hockey I have come to realise it is in my best interests and those of the Black Sticks to accept this opportunity and for someone else to lead this talented group of athletes through to Tokyo," says Hager.
"Ultimately, the opportunity to coach England/Great Britain is one that excites me with the quality of the teams, the wealth of competition on their doorstep in Europe and the resources available."
Hager said he has taken on board some feedback during the review period about his coaching style but will retain the essence of what has worked so successfully over the last decade in taking and keeping the team in the world's top five.
Hockey New Zealand chief executive Ian Francis said Hager has been an outstanding coach who has taken the performance of the Black Sticks women's team to unprecedented levels of success.
"When Mark took the reins in 2009 we were well and truly outside the world's top 10 countries.
"Since then he has taken this team to two Olympic fourths, two World League finals, a Champions Trophy bronze, and a medal of every colour at the Commonwealth Games. We have been ranked as high as third in the world and have never been outside the top six. These are by far the best results in the history of our women's game."