The left-back has signed a two-year contract at the King Power Stadium.
Bertrand, 31, left Southampton after seven years at the club earlier this summer after his latest deal expired.
"It feels amazing," he told LCTV. "I've had the first day today but I'm looking forward to getting started properly with the lads and I can't wait. It's complemented my inner ambitions and what I want to achieve still.
"There is no better place to be, to be honest, to be a part of what they've built over the years, and to continue that journey. Leicester have built something amazing over the years. Especially since Brendan's come in. He's added to that massively, in terms of the mentality.
"You can see the squad they've assembled as well… the professionalism, the standards, the values that everyone shares and buys into. They have one common goal, so it speaks volumes, and hopefully that'll leave us in good stead."
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