The 17-year-old attacker has signed with the French giants on a contract through June 2020, turning down reported interest from Chelsea, Milan, and other French sides.
Weah joined PSG in 2014 and has performed well for the club's youth sides, earning him his first pro deal.
"I am very proud to continue the adventure at Paris Saint-Germain by signing this professional contract," Weah told the club's official website.
"I am in a big club and I look forward to continuing to progress so that one day I can play for the first team."
The son of former Ballon d'Or winner George Weah, New York-born Timothy has opted to represent the United States at the international level, rather than his father's native Liberia.
Weah played for the U.S. at the CONCACAF Under-17 Championship earlier this year and is expected to be part of the team's squad at the U-17 World Cup in India in October.