Chelsea confirmed earlier this month that Christensen was to leave Stamford Bridge at the end of his contract, having contributed to 14 clean sheets in 34 appearances for Thomas Tuchel's men in the 2021-2022 season.
The writing had looked to be on the wall for Christensen when Tuchel revealed the defender opted out of featuring in last month's FA Cup final defeat to Liverpool for "private" reasons, with Barca strongly linked with a move for the 26 year-old.
Christensen joined the London club as a youth player when leaving Brondby in 2012, going on to win the Champions League, Europa League, UEFA Super Cup and FIFA Club World Cup with the Blues.
He has now opened up on the difficulties he faced in deciding to seek pastures new, writing on Instagram: "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."
Christensen made 93 Premier League appearances for Chelsea and spent two seasons on loan at Bundesliga outfit Borussia Monchengladbach between 2015 and 2017.