Bournemouth dismissed Parker in August after they were hammered 9-0 at Liverpool for their third straight defeat which left them fourth from bottom of the standings with three points from four games.
First-team coach O'Neil took over in the interim and presided over a six-match unbeaten run before a string of four losses. Bournemouth are 14th with 16 points from 15 matches after their 3-0 win over Everton earlier this month.
"We've been impressed with the way he has conducted himself from the moment he joined the club and feel he has earned this opportunity to continue to take the team and the club forward," Bournemouth chief executive Neill Blake said in a statement.
"Gary has worked tirelessly and diligently on the training pitch and the players have responded by producing some excellent performances and results.
"It was evident from the reception he received from our supporters following the Premier League win against Everton that they have also appreciated his efforts and we are all looking forward to continuing our working relationship with him."
O'Neil's new contract has the provision to be extended for a further 12 months.
Bournemouth visit Newcastle United in the fourth round of the League Cup on December 21st before a league trip to Chelsea, following the break for the World Cup.
