The Gunners agreed to terminate Bellerin's contract to facilitate a move.
Bellerin joined Arsenal from Barca as a 16-year-old in 2011.
He made 308 appearances for Arsenal, scoring 15 goals.
"During his 11 years with Arsenal, Hector won three FA Cups and made nearly 250 appearances – such a huge contribution to the club. I'm privileged to have played in the same squad as Hector for three seasons, wearing the Arsenal shirt and sharing many great moments on and off the football pitch together.
"We thank you Hector and wish you and your family all the best for your return to Barcelona."