The 20-year-old has spent this season on loan at Nigel Pearson's side and helped them win promotion to the Championship.
Hobbs has impressed during his time at the Walkers Stadium and has now inked a four-year contract with the Foxes for an undisclosed fee.
He told the club's official website: "I have thoroughly enjoyed my season with the club and I am absolutely delighted to make the move permanent.
"This is a massive club and I believe we can go all the way to the Premier League. That's one of the reasons why I have committed to signing a four-year deal.
"I couldn't be happier here. Leicester have shown great faith in me and instilled me with great confidence. I really am over the moon."