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Barrett, who has played eight seasons for the Hurricanes, is headed north to Auckland on a four-year deal, TVNZ has reported.
It is not yet known whether the new contract includes a rugby sabbatical like other big-name All Blacks contracts include.
Barrett and his wife, Hannah, are upping sticks from the capital later this year to base themselves in Auckland.
Barrett, whose father played for the Hurricanes, has been fiercely loyal to the club he first played for in 2011.
Barrett is understood to be planning to take both a non-playing and playing sabbatical as part of a four-year contract extension to stay in New Zealand.
It is probable that he will be granted permission to take an extended break from all rugby after the World Cup and miss much of next year's Super Rugby season.
He's expected to play in the latter weeks of the competition and be available for the July tests and Rugby Championship before then joining a Japanese club at the end of the year, where he will be based until May 2021.
It is, in essence, a similar deal to the one Brodie Retallick has been granted in that like the big Chiefs lock, Barrett is being afforded an 18-month window in which to enjoy a combination of time off and a lucrative spell in Japan before fully committing to New Zealand in May 2021.
The Blues have sought a quality No10 for many years, but for various reasons have either failed to recruit one – Barrett, Dan Carter and even former England international Jonny Wilkinson have turned them down – or develop their own. It is the one major reason why they haven't won a Super Rugby title since 2003.
The Blues, who have missed out on the Super Rugby playoffs for the eighth straight season, currently have three first-five options - Otere Black, Harry Plummer and Stephen Perofeta.
Barrett recently told Radio Sport Breakfast he hoped to be able to announce his plans soon.
He said when re-signing with New Zealand Rugby and the Hurricanes in 2016: "I love playing for the All Blacks and representing my country in the black jersey and I'm loving my footy at the moment.
"The All Blacks are an incredibly special team to be part of and I'm looking forward to playing my role and adding my small part to the legacy over the next few years.
"As well, with the Hurricanes, we've built a great culture at the club and it's an exciting time to be involved with a great bunch of guys and a quality coaching staff. Next year I'm looking forward to doing everything I can to help build on our success this year.
"I'm also a proud Taranaki man, proud of my roots and stoked to be recommitting to my home province."
Barrett married long-time partner Hannah Laity on Rakino Island, near Auckland in January.