Foster signed a four-year deal with Monaco, who are currently placed in position 19 on the French Ligue 1 standings.
The 18-year-old spent some time with the French Ligue 1 side late last year as the technical team wanted to assess him further.
Foster becomes Pirates' youngest player to move to one of Europe's top five leagues.
Augusto Palacios, who is currently the club's head of youth development, is delighted to see Foster move abroad.
“It is such an honour to see Lyle moving to a big club at such a young age. As a person who is passionate about youth development, this is the type of thing that makes the long hours all worth it,” Palacios told the Pirates website.
“Lyle came into my hands as a baby at 13 years old now here he is on the verge of making the biggest move of his career. I would like to wish him the best of luck and also thank the Foster family for their active involvement in their child's’ development.”
“Let this move pave a way for more such transfers in the future. For all the boys who will be part of the Project X tour of 2019, let this be an eye opener of what is possible if you make use of the opportunity when it presents itself,” he concluded.
Monaco also confirmed the deal on their official website.
According to Monaco, Foster will work with coach David Bechkoura at the club's reserve team.
Foster was only promoted to the Pirates first team last season, soon after being signed from the Walter Sisulu Discovery Games which are played annually in Soweto.
He became the youngest player to score on Pirates debut aged 17 against Polokwane City.
Foster joins fellow South Africans Keagan Dolly, Lebo Mothiba and Lebohang Phiri who are all plying their trade in France.
Pirates may be forced to go into the market and find Foster's replacement even though they appeared to be coping just fine without him this season.