Spurs entered advanced talks with the recently relegated Foxes earlier this week and secured the services of the England international on Wednesday in a deal worth Stg 40million ($A77 million) plus add-ons.
Maddison has agreed a five-year deal with the club and becomes Postecoglou's third arrival of the summer, but by far the most significant.
The transfer of Maddison represents 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 waned with his time at Leicester only serving to highlight 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 for 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.
Maddison's creativity and versatility will boost a Spurs squad that has lacked a player in his mould since Christian Eriksen left in 2020.
His arrival completes a busy couple of weeks for Tottenham, who made Dejan Kulusevski's loan switch from Juventus permanent and signed Empoli goalkeeper Guglielmo Vicario.
Speculation over the future of vice-captain Harry Kane continues, with Bayern Munich reportedly ready to submit a bid for Tottenham's record goal-scorer.
Kane is approaching the final 12 months of his contract, but Spurs have no intention of selling the forward this summer, it is understood.
Spurs are also to host a friendly with Shakhtar Donetsk at Tottenham Hotspur Stadium on August 6.
Funds from the match will go towards Shakhtar's charitable foundation to help with the ongoing humanitarian crisis in Ukraine following Russia's invasion.
Postecoglou said: "Shakhtar is a side that delivers domestic success on a consistent basis and will provide a perfect test for us ahead of the new season.
"However, as we all know, this match represents so much more than football - it's an opportunity for everyone at the club and our fans to come together in showing support and solidarity with the people of Ukraine during unimaginably difficult times.
"It promises to be a special occasion, for me personally, as it will be my first time in front of our home fans, and for the world to once again see how football has the unique ability to unite people in support of good causes."
11°C