Leicester have been locked in talks with Morgan over a new deal for some time as they looked to secure his long-term future.
Morgan has established himself as a key player in the Leicester side since arriving from Nottingham Forest in January 2012.
Leicester took up the option to extend Morgan's deal in January for a further year to keep him at the King Power Stadium until 2015, but now they have moved to extend it even further.
Morgan has signed a new three-year deal and follows the likes of Danny Drinkwater and Matty James who both signed new long-term contracts.
The news of Morgan's deal will come as a massive boost to Leicester boss Nigel Pearson as he plans for life back in the Premier League.
Morgan told the club's website: "I'm delighted to finally commit my future to this club.
"Winning promotion with this squad last season and lifting the Championship trophy were the proudest moments of my career and I can't wait to hopefully lead the team out on the opening day of the Premier League season.
"We've all worked so hard to win promotion and the whole squad is determined to make the most of it.
"There are some big challenges ahead in the next few years and I'm excited that I'm going to be part of it."
Pearson felt it was key to secure the player's future with an important season ahead.
"Wes has been every bit the captain we hoped he would be when we signed him two-and-a-half years ago," he said.
"He's a leader on and off the pitch, sets a terrific example for young players and is an extremely positive influence on the squad.
"He is one of number of players that has worked incredibly hard to reach the Premier League, both during his time at Leicester and throughout his career, and he fully deserves the opportunity to test himself at that level.
"I'm absolutely delighted that his long-term future remains with us."