Billing, 29, joined the Cherries from Huddersfield Town in the summer of 2019 and went on to make 201 appearances in all competitions, scoring 31 goals in the process.
During his five seasons on the south coast, he played an integral role in the side’s return to the Premier League in 2021/22, most notably assisting Kieffer Moore’s winner against Nottingham Forest on the night promotion was secured.
The Denmark international now returns to his home country to begin the next chapter of his career.
"It is fantastic to finally have everything sorted out. I am proud to be able to call myself an FC Midtjylland player, and I am happy to be back in Denmark."
"Midtjylland has shown a persistent interest in me in recent years, and I feel that now is the right time. I have always thought that if I were to join the Superliga one day, I would still have plenty of years at the highest level left in me. This is the perfect time."
"This club just makes sense. The commitment and interest they have shown in me – combined with the community, the family feeling, and the way the people at the club are."
"It will always be strange to go home after 13 years abroad – but there had to come a time, and the right time is now. The years have gone by quickly, many experiences and friendships along the way, but now a new great chapter is starting."
Billing could get his debut on Thursday night when FC Midtjylland face KuPS in the return leg of their playoff round clash in the qualification for the Europa League.