He expressed his excitement about joining the Merseyside club.
Marcus Rashford netted his fifth goal of the season thanks to a well-worked move involving Dani Olmo.
The Unify League is a breakaway league proposed in 2021 to rival the traditional UEFA Champions League.
Barça took the lead inside the opening minutes through a powerful solo effort from Robert Lewandowski into the bottom corner beyond Unai Simón.
The 18-year-old Spaniard edged out fierce competition to be crowned the best young player in world football for the second year running.
The Cameroon-born French footballer has been without a club since his departure from Lille at the end of last season.
It marked a fifth straight European final victory for the London club.
The result means Arsenal have progressed in 19 of 21 UEFA knockout ties after winning the first leg at home.
Real are now two points ahead of Barcelona, who have played a game more than both them and Atletico.
The victory will be a huge relief for Vinicius after losing the Ballon d’Or to Rodri.
