The 29-year-old made more than 200 appearances across six years in Dorset but leaves after falling down the pecking order in midfield under Andoni Iraola.
Last season, Billing played only around 300 minutes of football for Bournemouth and for Italian side Napoli, after joining the Serie A team on loan in January.
Billing was keen for a return to Denmark and was among the Cherries’ top three highest earners, so his departure follows the trend for Bournemouth this summer in moving on squad players to save on the wage bill.
This includes Neto, who left to join Botafogo in Brazil, and Luis Sinisterra, who has joined Cruzeiro in the South American nation, initially on loan but with an obligation to buy.
_(Image: Stuart Martin)_ Other players that were on loan last term and have moved on this season include Jaidon Anthony who joined Burnley and Joe Rothwell, who has moved to Rangers.
Billing joined Bournemouth in 2019 for £15m from Huddersfield, playing 201 times, scoring 31 goals and notching 20 assists under six different managers.
He has played a key role in many historic Cherries moments across his time on the south coast, including teeing up Keiffer Moore to score the winner against Nottingham Forest to secure Bournemouth’s promotion to the Premier League in May 2022.
But under boss Iraola, Billing has seen his minutes reduced.
Despite scoring the winner in Iraola's first league victory with the team and netting in the historic 3-0 win away at Manchester United, he started just 13 times in 31 appearances in Iraola’s first campaign at the Cherries, before making one start in 10 last term.
That prompted a loan move to Napoli, where he helped the side win Serie A, although again he made just ten appearances and only one from the start.
While Billing returned to Bournemouth for pre-season and was among the substitutes for the opening game of the season at Liverpool, he was left out of the second squad against Wolves at the weekend.
He now returns to Denmark to join FC Midtjylland.