Johnson, 23, has been dogged by several injuries since 2008 and was sidelined for all of last season.
He is reunited with manager Sven-Goran Eriksson, for whom he made 25 appearances at City during his breakthrough period in 2006-07.
Ghana international defender Pantsil has also joined Leicester, having signed a three-year contract following his departure from Fulham at the end of his deal at Craven Cottage.
“It’s very good that a player of John’s experience and quality wants to join us,” Eriksson told the Foxes’ official website.
“He is another established Premier League footballer with a lot of caps at international level.
“He’s very athletic, strong, and I’m sure he will do very well for us.
“If we lacked experience in defence last season, we have certainly addressed that with the players we have brought in this summer.”
Pantsil has made nearly 100 Premier League appearances since moving to West Ham in the summer of 2006, and then to Craven Cottage two years later.
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Manchester City loanee Michael Johnson follows John Pantsil to Leicester City