The 26-year-old will have a medical on Wednesday after Leicester accepted Spurs' offer for the England midfielder.
Leicester had hoped for around £60million, but dropped that asking price as they looked to rebuild their side to try and win promotion back to the Premier League.
The north London club has always been Maddison's preferred destination, despite interest from Newcastle.
The Magpies had been tracking him since last summer, but have not followed up that interest with a formal bid.
Newcastle failed with a bid last summer, but a pathway of sorts appears to have cleared for Spurs with the Magpies set to splash-out £60m on Sandro Tonali from AC Milan.
Read more on Tottenham
Bayern Munich in £60m Harry Kane move - but Tottenham set to reject any bids for striker
Postecoglou's backroom staff: New Spurs boss names team including Crystal Palace legend
Maddison has made 203 appearances for Leicester since joining them in 2018 and helped them to FA Cup glory in 2021.
He scored ten Premier League goals and registered nine assists last season, but was unable to prevent the Foxes from slipping into the Championship.
Maddison, who has won three caps for England, will become new manager Ange Postecoglou's third signing since joining Tottenham from Celtic.
Winger Dejan Kulusevski completed a permanent transfer from Juventus for around £25m.
Most read in Football
Arsenal send record Rice bid, Spurs confident of Maddison, Havertz announcement close
Arsenal make third British record £105m bid for Declan Rice
Former Liverpool starlet spotted training with non-league side during pre-season
Man City announce signing of Mateo Kovacic from Chelsea
Goalkeeper Guglielmo Vicario has also joined on a five-year contract from Italian club Empoli.
Current number one Hugo Lloris has 12 months left on his contract, but has signalled his intention to leave the club.