Christensen's Chelsea contract expires this month and the club have already announced his departure.
The 26-year-old's final few months in West London looked difficult as he reportedly opted out of matchday squads on a couple of occasions because of private reasons including the FA Cup final against Liverpool last month.
Christensen joined the club's academy as a teenager in 2012 before making his first team debut in 2014.
He had to bide his time before becoming a regular at Stamford Bridge, spending two years on loan in the Bundesliga with Borussia Monchengladbach between 2015 and 2017.
Christensen would go on to make 161 appearances in total for the Blues, winning a host of laurels, including the Europa League and UEFA Champions League.
In a post on Instagram, Christensen wrote: "I had a tough decision to make at the age of 16 to leave Denmark. There was only ever one choice for me and that was Chelsea. From the moment I arrived they made me feel at home.
"Some of my proudest moments at the club were when we won FA Youth Cup and UEFA Youth League. Those were a special group of young players that I was proud to have as team-mates.
"Last year was my proudest achievement as a player and team when we lifted the Champions League in Porto.
"I was a young boy at Chelsea with all the hopes and fears of a player starting his career, I'm grateful to the whole club for making my dream come true.
"Having spent 10 amazing years at this club, I felt now was the right time for a new beginning for me and my family. Mentally the last few months have been tough as it's not been an easy decision to leave this club and the fans.
"I'm not the most talkative person so sometimes people don't understand how much the club and the fans mean to me. I will miss the players, staff and everyone here. I wish the best for the club and the fans in the future."
