The 24-year-old has agreed a five-year deal and will link up with his new team-mates in early July before their pre-season training camp in Austria.
Maguire told the Foxes' website: "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.
"Leicester are on the up and it looks very promising for the future."
BBC Radio Humberside understands the deal comprises an initial £12m fee with add-ons.
Maguire's former club Sheffield United will also profit as they agreed a sell-on clause with Hull in 2014 - thought to be 10% of any fee over the £3m they received for the defender from the Tigers.
BBC Radio Leicester's Ian Stringer:
The Foxes are in urgent need of reinforcements in the heart of their defence. Captain Wes Morgan and Robert Huth have been brilliant, clearly playing through pain at times, but they need support.
Maguire ticks plenty of boxes. He has Premier League experience, plays plenty of games and does not seem to suffer injury too regularly.
It's a big summer for new boss Craig Shakespeare and this seems a very sensible start.
Find all the latest football transfers on our dedicated page.
Leicester City have signed Hull City defender Harry Maguire in a £17m deal.