The Magpies chased Botman in the January transfer window, but were left disappointed when Lille would not sell, and resumed the pursuit this summer.
Botman has preferred a move to AC Milan, with whom he has an understanding on personal terms, however Newcastle have now won the transfer scrap.
According to Dutch daily De Telegraaf, Botman will travel to Newcastle on Monday to undergo a medical with the club.
The Dutch Under-21 international will cost the Magpies an initial fee of €38m to take to St James’ Park.
The agreement also includes a further €2m in bonus payments, meaning Newcastle could end up paying €40m for the centre-back.
Botman has agreed terms on a contract with the Premier League side and it will run until the summer of 2027.
Newcastle will now look to quickly push the deal over the line and avoid any late hijack attempt from another club.
