O'Neil replaced Scott Parker last season, first on an interim basis, before being given the job full-time.
He steered them away from the relegation zone to a 15th place finish.
The 40-year-old took 36 points from his 34 top-flight games in charge.
O'Neil had been tasked with steadying the ship after Parker was axed in August following a 9-0 thrashing at Liverpool and public criticism of the board.
He impressed sufficently enough to be appointed permanent manager in November on an 18-month contract, and won 10 and drew six of his games at the helm to guide Bournemouth to safety.
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But despite earning widespread praise for the job he has done, O'Neil was informed on Monday morning that the club have decided to go in a different direction ahead of the new Premier League season.
AFC Bournemouth owner and chairman Bill Foley explained: "Gary's achievement last season is one I will always be grateful for. This has been a difficult decision, but it has been made with great consideration to best position ourselves ahead of the coming season.
"As a club, we have put plans in place for long-term success with improvements being made to infrastructure, most notably the development of a new state-of-the-art training facility and the ongoing discussions around upgrades to our stadium.
"We have also identified a number of significant targets in the transfer market this summer and believe this change in direction will provide us with the best platform from which to build.
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"Gary will go on to have a long career as a head coach or manager, but we feel that, at this moment in time, a change is in the best interests of this football club.
"I would like to place on record my thanks to Gary and wish him all the best for the future."
The club said the announcement of a new head coach will be made shortly.