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With automatic promotion effectively guaranteed, Bournemouth quickly showed their intent to push for three points through Callum Wilson, who forced a solid block from Addicks goalkeeper Stephen Henderson.
Moments later, the Cherries went in front through Ritchie, who curled the ball into the far corner after it had been teed up for him on the edge of the penalty area.
It took just two minutes for Bournemouth to double their lead as Arter capitalised on a mistake in the Charlton defence before calmly slotting the ball past Henderson from 12 yards.
Charlton improved after the restart, but it was Bournemouth who came closest to a third goal when Ritchie struck the crossbar after neat work in and around the penalty area.
Arter than dragged a shot wide from distance, before Yann Kermorgant had a strike deflected away for a corner as Charlton battled to remain in the match.
With three points seemingly secured, all eyes were on Vicarage Road, and the Bournemouth supporters heard the news that they were looking for when Sheffield Wednesday netted a 91st-minute goal against their title rivals.
Because of a lengthy first-half stoppage, the game at The Valley was several minutes behind the other fixtures and, as news filtered through, Ritchie fired through a pack of bodies to send the visiting fans wild.
After the full-time whistle had gone at Watford, Eddie Howe's men were able to enjoy the final few minutes before being confirmed as a Premier League club for next year.