ESPN's Adam Schefter first reported the news.
According to NFL Network's Ian Rapoport, the deal is worth $60 million. Rapoport also described the contract as "heavy on up-front money."
After spending most of his rookie season coming off the bench as part of Pittsburgh's defensive line rotation, Tuitt became one of the team's most important defenders over the past two years.
He made 28 starts, and Pro Football Focus noted his performance has gotten better each year of his career:
The 24-year-old Tuitt was entering the final season of his rookie contract and was set to make $1.05 million this year, per Spotrac.
"We're going to see," Tuitt said about his contract Wednesday, via Ray Fittipaldo of the Pittsburgh Post-Gazette. "I was just paying attention to practice today, so I didn't look at my phone yet. I'll see where we're at. Right now, we're just doing things day by day.
"It's ongoing. Hopefully, everything is close. Right now I'm worried about getting better every day to get ready for the Browns."
Since the Steelers don't negotiate contracts during the season, Tuitt and the team were facing a Saturday deadline to reach a new deal.
Tuitt has been an integral part of the Pittsburgh defense since he was drafted. He finished second on the team with 6.5 sacks in 2015 and followed that up with four sacks to help the team reach the AFC championship game in 2016.
With Tuitt locked up for the future, the Steelers' outlook remains bright as they seek to remain atop the competitive AFC North for years to come.