Philippe Coutinho has scored against Manchester United, Leeds (2) and Southampton since joining Aston Villa on loan
The Brazilian, 29, moved to Villa Park on loan in January in a deal which included an option to buy at the end of the season.
He has now signed on a contract running until 2026 for 20m euros (£17m) and is understood to have taken a considerable wage cut from his deal in Spain.
"This is a brilliant signing for Aston Villa," said manager Steven Gerrard.
"Phil is a model professional and his impact on the group has been very clear since he joined in January.
"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."
Coutinho has scored four goals and provided three assists at Villa, although none of those have come in his past eight games.
He joined Barcelona in a £142m move from Liverpool in January 2018 and had 12 months to run on his contract.
Gerrard, who was Coutinho's captain at Liverpool, made it clear after Saturday's impressive 3-1 win at Burnley that he wanted to sign Coutinho permanently.
Coutinho scored 54 goals in 201 appearances for Liverpool, who he joined in a £8.5m move from Inter Milan in January 2013.
He scored 26 goals in 106 appearances for Barcelona.
-- Courtesy of BBC Sport