"Juventus and the player have signed a 5-year contract of employment until 30 June 2024," a statement said.
"Juventus has reached an agreement with Genoa for the free loan until 30 June 2020 of the registration rights of the same player and bonuses of maximum €5.3 million will be paid to Genoa on achieving given sports performances."
Romero, 21, played 27 games, scoring twice, in his first campaign in Italian football after joining Genoa from Belgrano in his native Argentina in July 2018.
The Stade Luigi Ferraris side only maintained their status in the Italian top flight thanks to a superior head-to-head record with 18th-placed Empoli.
The youngster is Juve's sixth close-season signing after midfielders Aaron Ramsey and Adrien Rabiot, defenders Merih Demiral and Luca Pellegrini as well as the return of legendary goalkeeper Gianluigi Buffon.
Juve have won eight straight Scudetto titles but Maurizio Sarri's side have failed to lift the Champions League since 1996.