Quinn's turbulent four-month reign was brought to an end following a meeting with the club's owners at the Royal Bath Hotel on New Year's Eve.
The 49-year-old Ulsterman had refused to quit after calls for his head had intensified following the Cherries calamitous defeat to relegation rivals Barnet the previous Sunday.
But with the club's Football League status under threat and the team on a downward spiral, the Cherries board acted swiftly to relieve Quinn of his services.
Quinn, who succeeded Kevin Bond at the start of September, took charge of just 24 league and cup matches, with the Cherries winning five and drawing seven of their 19 league games.
Eddie Howe, who worked under Quinn's predecessor Bond, will take charge of team affairs for the clubs trip to Darlington this Saturday. He is expected to be assisted by the club's head of youth Joe Roach.
Meanwhile, decisions have yet to be made on the futures of assistant boss Jason Tindall and director of football operations Ted Sutton.
Quinn's was the shortest managerial reign at Dean Court - by some considerable margin - since the club joined the Football League in 1923.
He presided over the clubs disastrous FA Cup exit at the hands of non-league minnows Blyth Spartans earlier this month, which cost the club around £250,000 in lost revenue.