After his Chelsea departure was confirmed, Christensen wrote on Instagram: "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."
The Danish international, who played 161 games in all competitions for Chelsea, becomes the second senior centre-back to leave the club this summer after Antonio Rudiger's free transfer to Real Madrid.
Christensen's arrival at Barcelona was announced just hours after the Spanish giants confirmed the signing of Kessie.
The 25-year-old, who had been playing for AC Milan since 2017, is set to become just the second Ivorian to play for Barcelona after Yaya Toure.
Kessie joins Barca having helped AC Milan win their first Serie A title in 11 years last season.
Sky Sports News reported Tottenham were interested in signing Kessie in the January transfer window and were in talks with the former Atalanta man about a free transfer in the summer.
The Catalans, however, wrapped up a deal for Kessie weeks ago but needed to balance their Financial Fair Play ratio before they were able to register new players in their squad.
Last week, the club agreed to sell a 10 per cent stake in their La Liga TV rights for the next 25 years to US private equity group Sixth Street for £178.5m.