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Darije Kalezic announced last week he would not continue in his role next season after a disappointing tenure that has returned four wins, five draws and 12 losses.
He initially appeared ready to see out the six games remaining in the season, but a Phoenix statement yesterday said the Dutchman would now finish up immediately.
Both parties agreed it was in the club's best interests.
``I would like to thank the club and the staff for their support, and especially the city's loyal fans, Yellow Fever, for their passion,'' he said.
``I have had a great experience in New Zealand. I came with big determination and energy for this project, and I continue to believe that success can come for this football club.''
Greenacre, who scored 17 goals in an 84-match career at the Phoenix, filled in for five games in February, 2013 when coach Ricki Herbert resigned.
Alongside Des Buckingham, he also stepped up after Ernie Merrick's ninth-round resignation in December, 2016.
The Phoenix, which had a bye last weekend, meets sixth-placed Western Sydney Wanderers in Sydney tomorrow.
West Ham defender Winston Reid is expected to miss the rest of the English Premier League season after injuring his knee four days ago.
The All Whites skipper needed oxygen as he was stretchered off the field in the first half of Sunday's 4-1 defeat by Swansea City, his first game in almost two months.
Reid attempted to make a last-ditch tackle on Swansea's Mike van der Hoorn before getting his foot stuck in the ground and forcefully twisting his knee.
The absence of the 29-year-old New Zealander is a major blow to the Hammers' bid to stay in the Premier League.
West Ham is 14th on the EPL ladder, three points above the relegation zone, with nine games remaining