Juve said the fee can increase by a total of 3.1 million euros in bonuses based on sporting goals met as the club looks to replace the long-serving Colombian Juan Cuadrado, who left at the end of his contract.
Weah, who started his senior career at Paris St Germain, spent four seasons at Lille where he made more than 100 appearances, winning league titles with both teams.
He also won the league and cup double with Celtic when he was on loan at the Scottish side in the 2018-19 season.
"At Lille he won the French championship in the 2020-21 season and the French Super Cup the following year," Juventus said in a statement.
"Six consecutive years brimming with victories have transformed Timothy into a versatile player, capable of covering both defensively and in attack, making him an all-round wing-back."
Weah has played 29 times for the United States, scoring four goals and will be the second Weah to play in Italy after his father George, a former Ballon d'Or winner who scored 58 times for AC Milan and is the current president of Liberia.
He has signed for Juve on the same day French forward Marcus Thuram (25), son of Parma and Juve great Lilian Thuram, joined Inter Milan.