Spurs entered advanced talks with recently relegated Leicester earlier this week and have now struck a deal for the England international, the PA news agency understands.
Maddison will move to Tottenham in a transfer worth STG40million ($A77 m) plus add-ons, having already agreed personal terms.
The signing of Maddison will represent a major coup for Spurs, who have been long-term admirers of the 26-year-old.
Ex-Tottenham boss David Pleat recommended Maddison to chairman Daniel Levy when the playmaker was still a teenager at Coventry, but no move was able to materialise and he instead joined Norwich.
Spurs' interest and desire to eventually sign Maddison never waivered with his time at Leicester only serving to prove he was one of the most creative players in England.
During five largely successful years with the Foxes, who won the 2021 FA Cup, Maddison made 203 appearances, scored 55 goals and produced 41 assists.
While Maddison was unable to prevent Leicester suffering a shock relegation to the Championship last season, he was still able to hit double figures in terms of goals.
Leicester's battle for survival saw them turn down advances for Maddison in the January transfer window but they have now agreed for him to depart.
Newcastle had registered an interest in bringing the midfielder to St James' Park but decided to pursue a move for AC Milan's Sandro Tonali, which left the door open for Tottenham to swoop for their key target.
Maddison's creativity and versatility will boost a Spurs squad that has lacked a player in his mould since Christian Eriksen left in 2020.
Once his medical is completed, Maddison will become new boss Postecoglou's third signing following Dejan Kulusevski's permanent transfer and Tuesday's arrival of Empoli goalkeeper Guglielmo Vicario.
9°C