The former German international, who has penned a three-year contract at the King Power Stadium, initially joined the Foxes on loan during the January transfer window and played a pivotal role in helping the Midlands outfit retain their top flight status.
Nigel Pearson's side defied the odds by gaining seven wins and three draws in the final 14 Premier League games Huth appeared in, after being rooted to the bottom of the table for much of the campaign.
In total, Huth made 188 first team appearances for the Potters in all competitions after joining from Middlesbrough in August 2009.
He scored his first City goal against Everton in October 2009 and played a crucial part in the Potters' progress to the 2011 FA Cup Final, scoring the second goal in the 5-0 victory over Bolton Wanderers in the semi-final of the prestigious competition.
City Chief Executive Tony Scholes said, "Robert has been a fantastic player for the Club and a real fan's favourite.
"He's played a major part in the Club's progression over the last few years and we wish him all the very best for the future."