Two goals from Matt Ritchie and one for Harry Arter sealed the win and capped a memorable season for Eddie Howe’s side.
They finished a point clear of Watford at the top of the table.
Bournemouth will take their place in the top flight of English football having been close to liquidation in 2008 and a game away from going out of the Football League in 2009.
But under manager Howe, they have now earned three promotions, two of which have come in the past three seasons, and a spot in the top division for the first time in the club’s history.
Howe, 37, also joins a select band of managers to guide a team through the Football League and into the top flight, where they will earn an estimated £120m from their promotion.
Goals have been a feature of Bournemouth’s season and they were 2-0 up within 12 minutes at The Valley.
Ritchie found the net with a stunning low 25-yard strike which cannoned in off the far post while Arter, returning to this former club, neatly placed past Stephen Henderson from the edge of the area following a defensive mistake.
Those goals temporarily lifted the Cherries to the top of the table but hopes of the title were temporarily dashed as Watford took the lead.
Roared on by the vociferous away support of 4,000 fans, Bournemouth continued to pour forward in search of more goals.
Charlton, who will end the season in 12th, improved after the break without testing Cherries goalkeeper Artur Boruc, while Ritchie’s deflected effort came back off the crossbar.
Bournemouth’s fans chanted the theme music to Match of the Day and they were soon celebrating again after Ritchie’s persistence saw him lash home from 12 yards.
Moments later, the away end erupted again as news of Wednesday’s equaliser filtered around the stadium.
The final whistle at Vicarage Road confirmed Bournemouth’s achievement, while the conclusion of their own game brought wild celebrations from supporters and players, with both sets of supporters applauding the Cherries on their lap of honour.