The Premier League duo were both reportedly keen on obtaining the services of the 20-year-old, with the Magpies having a bid rejected for the French winger at the weekend.
Thuavin has instead opted to stay in Ligue 1 and signed a four-and-a-half-year deal with Lille, but will remain with Bastia until the end of the season.
"I am very pleased to join Lille," Thauvin told Lille's official website.
"Lille offered me a beautiful sporting project, and I immediately liked it and with the support of my advisors we agreed straight away."
Thauvin joined Bastia from Grenoble in 2010.