The Andalusian team paid €1.5 million up-front plus a potential further €9m in variables for the 32-year-old.
He played 310 games for Barcelona since joining them from Sevilla in 2014 and won 13 trophies with the Catalan side.
During that time he also scored 35 goals and made 42 assists.
Sources told ESPN on Monday that Rakitic would not attend Barcelona coach Ronald Koeman's first training session after completing a medical with Sevilla.
The Croatia international, who has 105 caps, saw his game time noticeably reduced during the 2019-20 season.
Rakitic has never hidden his desire to eventually return to the city of Seville, where his wife is from, or his affection for Sevilla, where he spent three successful seasons from 2011 to 2014.
Barcelona will hold a farewell ceremony and news conference for Rakitic on Wednesday.