The deal is worth $36 million, including $23 million guaranteed, a source said.
Delpit was a second-round pick out of LSU in 2020. He missed his entire rookie season with an Achilles injury suffered during training camp.
But Delpit bounced back to win a starting job in Cleveland's secondary the following season.
He has 35 career starts and leads Cleveland with 74 tackles entering Sunday's game against Jacksonville.
247Sports first reported the extension.