League sources told ESPN's Adam Schefter that the deal is worth $43 million.
"We think very highly of Tyler and are thrilled to get him in the fold for the next few years," head coach Zac Taylor said in a team release.
Boyd broke out in 2018, catching 76 passes for seven touchdowns while recording his first 1,000-plus yard season. He was set to enter the final year of his rookie contract before agreeing to the extension.
Boyd's annual salary of $10.75 million after the reported agreement would rank 19th among receivers, a shade below No. 1 wideouts Larry Fitzgerald and Emmanuel Sanders, and ahead of Sterling Shepard and Tyler Lockett.
The Bengals will next look to reach a new deal with star receiver A.J. Green, who's entering the final year of his contract.
"We'd like to get them both done," said Bengals director of player personnel Duke Tobin, according to Bengals.com's Geoff Hobson.