The 22-year-old will sign a five-year contract at the Saint James' Park and become manager Eddie Howe's third summer signing.
Newcastle will pay up to £35m for Botman, who was also the subject of interest from Serie A champions AC Milan.
Botman joined Lille from Ajax Amsterdam in the summer of 2020, making 79 appearances.
He helped Lille win the Ligue 1 title in the 2020/2021 season.
A Newcastle statement read: "Newcastle United have agreed a deal in principle with LOSC Lille to sign Dutch defender Sven Botman for an undisclosed fee, holding off competition from a host of European sides to secure the highly-rated centre-back.
"Botman has completed his medical on Tyneside and agreed the terms of a five-year contract.
"The formalities of the transfer are set to be concluded this week, following which the 22-year-old will officially become a Newcastle United player."
Botman is yet to win a senior cap for the Netherlands national team.
Newcastle have already signed Matt Targett permanently from Aston Villa following a loan spell and goalkeeper Nick Pope from relegated Burnley.
