Fuchs has agreed a one-year deal with King Power chiefs until the end of next season.
The 33-year-old left-back joined Leicester on a free transfer in 2015 after leaving German club Schalke. He has made more than 100 first-team appearances.
Fuchs, a key member of Leicester’s 2015/16 Premier League title-winning squad, has won 78 caps for Austria and captained his country.
“I’m thrilled to be signing a new one-year deal with Leicester City Football Club,” he told the club’s website.
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“It’s an exciting time for everyone, with a new training ground being built and some fantastic young talent coming through.
“Our ambition is to play good football and continue to improve.
“The club and our fans have always been great with me, and I want to give back as much as possible.
“I can’t wait to see what next season brings for this football club.”
Meanwhile, two members of their title-winning squad – defender Simpson and forward Okazaki – will leave the club at the end of this season.
They made more than 260 first-team appearances between them, with right-back Simpson joining Leicester from Queens Park Rangers in 2014 and Okazaki arriving from Mainz the following season.