The former All Black captain will continue in his post until a replacement coach has been identified.
As he prepares to depart, the Gunners have signed former Llanelli Scarlets and Waikato Chiefs lock Dave Duley for the remainder of the season.
Blackadder said: "Edinburgh has been a huge part of my life and I will always have a real emotional attachment to this beautiful city and more importantly to the club.
"The people I've played and worked with here feel like a part of my family and I've made some lifelong friends.
"I can see some great things happening here in Scotland and it's disappointing that I won't be part of that.
"For both the Edinburgh Gunners and Scottish Rugby, things are turning for the better and I have real belief in Gordon McKie (chief executive) and Frank Hadden (Scotland coach) to take rugby in Scotland forward in the right direction.
"I have seen some fantastic rugby played here by Edinburgh and we are as good a team as any in Europe.
"We also have a passionate group of fans who I will miss greatly.
"I have received countless letters and emails from them over the years and always enjoy a chat with them after matches at the stadium."
He added: "Until my post has been filled nothing will change here. The Gunners are a winning team and I'm fully committed to ensuring that continues."
Duley, who turned 29 on Boxing Day, meanwhile will assist the Gunners for the remainder of the season in their Celtic League title chase alongside current locks Alastair Kellock, Fergus Pringle and Scott Murray.
Duley said: "I'm very pleased to be involved with the Gunners and really looking forward to playing at their high standard. It's a big year for them and I'm keen to play my part and hopefully help them lift the Celtic League title.
"I like the way the Gunners play and Edinburgh is an awesome city, so I'm very happy to be here. My first game for the Scarlets last year was against Edinburgh up here at Murrayfield and we lost 23-0 so I know this is a quality side with a lot to offer."