The pair took the reins when Ernie Merrick resigned four weeks ago and have been in charge for four games that have seen the team unbeaten in winning one and drawing three.
On Sunday night the Phoenix fought out a scoreless draw with defending champions Adelaide United and were only denied a win by some outstanding saves from United keeper Eugene Galekovic.
Under the FFA regulations Buckingham, who holds a Pro Licence, will be head coach and Greenacre, a former striker with the club who has an A Licence, will be co-coach.
Buckingham said he was looking forward to the challenge.
“I still think this team is capable of making the top four which was our aim at the start of the season,” he said.
“It is good that we have gone four games unbeaten, which I’ve been told hasn’t happened since February 2015, but we could have won all three with a bit of luck.
“We have been handed a fantastic challenge and have been fortunate to have worked with Ernie Merrick who upskilled us and exposed us to a lot of stuff that wouldn’t have happened with other coaches at other clubs.’’
Greenacre, a former Manchester City and Tranmere Rovers striker who was a Phoenix fan favourite in his playing days, said he was pleased to have the coaching situation decided.
“To lose our mentor was tough but that is the nature of the game of football and it has presented us with a fantastic challenge and life is all about challenges”, he said
Wellington Phoenix Chairman Rob Morrison said the club Board were confident that the newly appointed coaches could take the club forward positively.
“We interviewed a number of excellent candidates but with the run of games we have through January, we felt it was too difficult for any new coach to get to grips with a new squad and the challenges of coaching in the A league,” Morrison said.
“We have a really good squad and Des and Chris impressed with their views on what needed to change and how to get the best from the squad.
“The board are confident that Des and Chris can take the team through to the playoffs.”