George Weah played for PSG from 1992 to 1995, the year in which he won the world player of the year award, before joining AC Milan.
Timothy Weah has penned a deal with the Ligue 1 side that will keep him at the Parc des Princes until 2020 – and the 17-year-old is keen to progress.
“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 I can one day play for the first team.”
Weah has shone in PSG’s youth set-up since joining the club in July 2014. He scored a hat-trick in an 8-1 thumping of Bulgarian side Ludogorets on his UEFA Youth League debut in September 2016.
Weah went on to make four appearances in the 2016/17 competition, before PSG were eliminated in the round of 16 by eventual winners Red Bull Salzburg.