£500,000, which could increase to £750,000.
Hume has rejected moves to North End and Sheffield Wednesday in the past but felt it was the right time to leave Rovers - the club he joined more than six years ago.
"I never really said I wanted to leave Tranmere but I said to the manager
(Brian Little) if something came up then I'd like to know about it," Hume said.
"I've been there since before I was 16 and I've been there a long time
so I'm sad to be leaving but it¹s probably the right time for me."
He added: "Leicester are a massive club. They've been in the Premiership in
recent years and hopefully we can get back there. The stadium holds
more than 30,000 and the training facilities are second to none."