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Pagano was facing an uncertain future after the Colts missed the NFL play-offs for the first time since 2011, some reports suggesting the 55-year-old could be relieved of his duties as soon as Tuesday.
However, the Colts have opted to retain Pagano after careful consideration following lengthy meetings with owner Jim Irsay on Monday.
"I've had a lot of great days in my life, but none better than today. This is absolutely the best day of my life," Pagano said in a news conference.
"I'm grateful to Mr. Irsay for the opportunity. He's stood behind me and never gave up on me.
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"Given this opportunity to move forward... words can't describe how I feel right now. It's a great, great day."
The Colts beat the Tennessee Titans in their final home game on Sunday to finish the season at 8-8.
Pagano, who led Indianapolis to identical 11-5 marks in each of his first three seasons, has a 41-23 regular-season record and a 3-3 play-off mark, without a single losing season on his resume, during his four seasons as coach.
"My focus was always on winning," Irsay said. "You'd like to have continuity if you can have it. This wasn't fan pressure or player pressure. Chuck's won 44 games the last four years."
An apparent tumultuous relationship with general manager Ryan Grigson created a culture of dysfunction in Indianapolis.
Grigson had reportedly undermined Pagano when he wanted to discipline certain players and even insisted that former running back Trent Richardson play to create a narrative that it was a good trade to send a first-round pick to Cleveland in 2013.
Irsay said Pagano insisted that he and Grigson remained "tied at the hip" and the latter was also given a new contract extension.
"Chuck Pagano is a great man. We've been through the ringer together, but we're still focused on one goal," Grigson insisted. We're united and have our eyes set on championships."