The new deal is worth $8.55 million per season, with an annual maximum value of up to $10.05 million, a source told ESPN's Adam Schefter.
"I've made it clear over the past year that I want to keep playing and I want to play here," Olsen said in a statement Thursday. "Both sides were very fair and worked on it in a timely manner. I feel really good about what we were able to get done both for ourselves and the team."
Olsen, who last month interviewed for the Monday Night Football analyst job previously held by Jon Gruden, was entering the final season of a three-year extension he signed in March 2015.
He told ESPN recently that he wanted an extension with the Panthers and would prefer to end his career in Carolina.
The 33-year-old Olsen missed nine games last season with a broken foot suffered in Week 2. It was the first time since his rookie season with the Chicago Bears that he missed a game and the first time since his first season with the Panthers (2011) that he missed a start.
Olsen is the only tight end in NFL history to have three consecutive seasons (2014-16) with at least 1,000 yards receiving.
The timing of the extension, on the eve of the NFL draft, is interesting. Now the Panthers might not be in the market for a tight end with the 24th pick.
According to a source, however, "nothing is off the table" in the first round, including tight end.
That doesn't mean the Panthers will select South Carolina tight end Hayden Hurst, as was predicted Tuesday night in the ESPN.com NFL Nation mock draft. They have plenty of other needs that are more pressing. A tight end to play opposite Olsen could be considered a luxury pick, even though Carolina plays a lot of two-tight-end sets and has no proven backup for Olsen after letting Ed Dickson go to Seattle in free agency.
The Panthers still have needs for a safety, wide receiver and possibly a center or guard.
Information from ESPN's David Newton was used in this report.