Brown spent the last four months of the season on loan at The Walkers Stadium and alongside Jack Hobbs in central defence, helped The Foxes claim top-spot.
The pair were on loan at The Walkers Stadium, Hobbs from Liverpool and Brown from Hull.
Hobbs sealed his permanent move last week and now manager Nigel Pearson has quickly tied up the signing of Brown.
"I am obviously delighted to have made the move permanent. Leicester City are a big club with an ambitious chairman, a good manager and a massive fan base," said the 31-year-old.
"It was great to finally get our hands on the League One trophy on Friday evening.
"There is a really good attitude here and we all want to continue to move forward and progress once again next season."