Wellington said Greenacre was in ongoing discussions with the New Zealand club about the head coaching position for the rest of the A-League season and beyond.
England-born Greenacre, who played 84 matches for the Phoenix from 2009-12, was interim coach in 2013, 2016-17 and most recently in 2018.
He steps up from his role at the team's academy where he has been head of professional development and coach of the Wellington reserve team which competes in New Zealand's domestic National League.
"It’s not the first time I’ve done this, but it doesn’t get any easier," Greenacre said in a Phoenix statement on Monday.
"Coming in this morning was quite difficult for me. We have to move on quickly as a club, but you never forget what’s gone before you."
The Phoenix are also looking for a new assistant coach, with Brazilian Kelly Guimarães resigning along with Italiano.
Italiano, who had been in charge since April 2023, announced his resignation at the post-match press conference following the home defeat against Auckland.
Wellington are 11th in the 12-team A-League table, with five wins from 18 matches, ahead of Sunday's home match against third-placed Sydney FC, who are led by former Phoenix coach Ufuk Talay.