Morgan famously skippered Leicester to the Premier League title in the 2015/2016 season under manager Claudio Ranieri. He was also a late substitute as the Foxes defeated Chelsea 1-0 in this season’s FA Cup final.
Morgan moved to the King Power Stadium in January 2012 and has so far made 324 appearances for the club, scoring 14 goals.
His involvement in the Leicester first team has diminished this season, with the likes of Wesley Fofana, Caglar Soyuncu and Jonny Evans ahead of him in the pecking order.
Morgan has made just 10 appearances for Brendan Rodgers’ side this season.
"This group came together to create something that I'm not sure will ever happen again, a team like Leicester, at that time, winning the Premier League against all odds," Morgan told Leicester's official website.
"It's something that doesn’t really happen but we made it happen. It was a very, very special moment for everybody involved.
"To win the Premier League, it was amazing and something you can never talk enough about."
Leicester chairman Aiyawatt Srivaddhanaprabha added: "Wes has been one of Leicester City's greatest servants, leading the team through the club's most successful era and helping to set the standards that have pushed the club forward.
"A big brother to everyone he has played with, a strong representative of the squad and a valuable source of counsel to managers and senior executives in the club, his contribution has been enormous.
"Wes has shown throughout his Leicester City career that he has a great deal to offer away from the pitch.
"I'm excited to see how we can help him shape his career after football and how the club can continue to benefit from his experience, knowledge and passion for the game."
