Maguire, 24, will link up with his new teammates in early July ahead of a pre-season training camp in Austria.
The centre-back becomes Craig Shakespeare's first signing since he agreed a three-year contract to remain Leicester manager last week.
Spurs scouts were reported to have kept tabs on Maguire and were sufficiently impressed with his performances to recommend him to club chairman Daniel Levy and manager Mauricio Pochettino.
However, Leicester have beaten their rivals to the punch, with the BBC reporting that the Foxes would pay £17m ($22m) to Hull for the defender.
Maguire told Leicester's official website: "It's obviously a very exciting time for myself. Once I had my eyes on this club, I always wanted to join. Thankfully I'm here so I can't wait to get the season started and kick on.
"There were a number of clubs interested, but when I met the manager here, he pretty much swayed it into the direction of this club. He showed me the way that the club is going. It's on the up and it looks very promising for the future, so credit to the gaffer.
"You can see that with the structure of the club, it's going to look upwards rather than down so that was a big reason why, as soon as I knew there was an interest, I wanted to jump at the opportunity."
Maguire's former club Sheffield United stand to receive 10% of the transfer fee received by Hull, as they had inserted a sell-on clause in the deal that took the defender to the Tigers in 2014.
Maguire will compete with Robert Huth and Wes Morgan for a place in Leicester's starting line-up.