Milne stressed that the Scotland assistant manager's departure "with immediate effect" was a mutual decision arrived at after two days of extensive discussions and soul-searching.
Milne confirmed at a hastily-convened news conference that Miller's increasingly inglorious battle to arrest the club's slump in fortunes was at an end after a run of just one win in 16 games.
The 3-0 home defeat by Dundee United late last month brought pressure to bear on the 49-year-old Miller and Saturday's humiliating 4-0 defeat at Kilmarnock appears to have been the last straw.
That result sent Aberdeen to the bottom of the Premier League and left Milne contemplating a change of manager for the second time in just over 12 months after Roy Aitken's departure last November.
Miller appeared to have steadied the ship as the Dons retained their top-flight status last year and briefly topped the new SPL at the beginning of this term.
But an overall record of just 11 wins from 43 games had already left the former Hibernian manager facing the wrath of disgruntled supporters unhappy at the team's dour style under his command.
Chairman Milne was forced to deny last week that a group of wealthy local businessmen - who form the affluent AFC Club at Pittodrie - were poised to launch a takeover bid unless action was taken to tackle the club's plight.
Miller appears to be have been made the scapegoat, but Milne was anxious to stress his exit was by mutual consent. "I would like to make it clear I haven't sacked the manager but that we have agreed that it is right that he moves on at this time," he said.
"We have spoken for some time over the past two days discussing matters and we have come to the conclusion, jointly, that it is in everybody's interests that Alex parts company with us.
"From a personal point of view, I am obviously very disappointed at the way things have turned out. But I would like to take this opportunity to thank Alex for all the hard work he has put into this club and I wish him all the very best in his future career."
Miller, who has resisted the temptation to complain about the lack of substantial funds available for team rebuilding in recent weeks, was happy to concur with his former chairman.
"After a substantial amount of talking and soul-searching, both the chairman and myself came to the conclusion that it would be in everybody's interest if I left the club," he said. "I have enjoyed my time here at Pittodrie and I wish Aberdeen every success in the future."
Milne confirmed that the assistant manager, Paul Hegarty, and the director of football, Keith Burkinshaw, will look after team affairs while the Pittodrie board ponders its choice of successor.
"They are both vastly experienced and they will continue to look to bring players in who they feel will be valuable additions to our squad," said Milne. Hegarty may be considered as a contender for the vacant job.Reuse content