0330 GMT February 18, 2020
The Cameroon star's five-year deal is subject to him getting a work permit.
The initial fee is expected to be around £10m, and comes less than 24 hours after the club sold Roberto Soldado to Villarreal for £14m, uk.sports.yahoo.com reported.
Add-ons expect to cost Tottenham another £2m.
N'Jie scored eight times in 33 appearances for Lyon last season as they finished second in Ligue 1.
He told the club website, "I'm very happy to join Tottenham, such a big club in England. I'm still young, still growing up and it’s a big challenge — the Premier League is one of the biggest leagues in the world.
"The club is ambitious and I’m ready to give my best to help the club achieve its aims. Like I said, I’m still learning and I’m here to give my best. I just hope I get the chance to give to the club what they are giving to me."
Njie is Spurs' fourth summer after Kieran Trippier, Toby Alderweireld and Kevin Wimmer.