Foster saw off a strong challenge from Crusaders head coach Scott Robertson and has been given a two-year deal.
"The NZR Board has today ratified Ian Foster as the new head coach of the All Blacks from 2020. He brings world-class international experience to the role, an incredibly strong coaching team, and we think he'll do an outstanding job.," Impey said.
"The interview process was extensive and really difficult, which reflects the very strong applications from both candidates."
Impey said Foster would be joined by four other coaches, who will be announced in due course.
"While we can't confirm the full make-up of the coaching team today, we're delighted with the quality they bring − they have a wide range of coaching experiences and are a diverse group of thinkers."
Foster's victory is one for continuity, New Zealand Rugby's board and interviewing panel deciding to go with a man who has been involved with the All Blacks since 2012 rather than the fresh outlook Robertson would provide.
The assumption will be that Foster re-signs after two years to take the All Blacks to the next World Cup in France in 2023.
Robertson recently re-signed with the Crusaders for another two years but will now almost certainly depart New Zealand for an overseas coaching job once that term expires. Lucrative job offers from French or English clubs will not be in short supply given his excellent Super Rugby record.
Robertson took an under-performing Crusaders team to a championship in 2017, his first year in charge, and has since won two more titles in two years.
Foster's last job as a head coach was at the Chiefs before Dave Rennie's successful reign. While Foster didn't have much success there, he has developed enormously with the All Blacks and the board has obviously decided that experience is too good to pass up.
Following the All Blacks' semifinal failure against England at the recent World Cup in Japan, there is an echo of Foster's appointment in the re-signing of Sir Graham Henry and company following the 2007 World Cup flop at the quarter-final stage against France.
Foster worked well with Hansen and wasn't afraid to challenge him occasionally, most obviously when insisting Rieko Ioane be given a chance for the All Blacks against the British and Irish Lions in 2017.