Barcelona said they had accepted a €20 million transfer fee with Barca also inserting a sell-on clause of 50% for any future transfer. Coutinho, who joined Villa on loan in January, became Barcelona's record signing when he joined from Liverpool for €160m in January 2018.
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In a statement, Barcelona said they "would like to publicly state their thanks to Philippe Coutinho for his commitment and dedication, and wish him success and all the best for the future."
Sources told ESPN earlier this week that Villa had an option to sign Coutinho for €40m at the end of the season but were not willing to invest so much money.
Aston Villa is delighted to announce the permanent signing of Philippe Coutinho from Barcelona for an undisclosed fee! 🙌— Aston Villa (@AVFCOfficial) May 12, 2022
Coutinho, 29, accepted a wage cut to join Villa in January due to his desire to play regular football again having fallen down the pecking order under Barca coach Xavi Hernandez.
At Villa Park under his former Liverpool teammate Steven Gerrard, he has scored four goals and supplied three assists in 16 Premier League appearances.
"This is a brilliant signing for Aston Villa. Phil is a model professional and his impact on the group has been very clear since he joined in January," Gerrard said in Villa's announcement.
"With the way he conducts himself on and off the pitch, he's also a valuable role model for our younger players who can only benefit from his experience.
"As we look to build towards next season, it is incredible to work at a club that executes its business so decisively and smoothly."