On his Twitter page Wednesday, Durant said that "God Is Great, me and my family came a long way."
Durant's agent, Aaron Goodwin, told ESPN.com's J.A. Adande the deal will be worth about $86 million over five years. The specific amount will be determined when the salary cap numbers are finalized on July 8, when Durant can officially sign the contract.
"Kevin wanted to make this commitment to the Thunder because he and his family are very appreciative of the commitment that the Thunder have made to him," Goodwin said of the five-year arrangement.
The deal does not contain an opt-out clause after the fourth season, which means Oklahoma City holds Durant's rights through the 2015-16 season. The new contract kicks in starting with the 2011-12 campaign.
"The Thunder showed the Durant family from the very beginning, at 11:01 [Central time] the first night, that they were committed to keeping him," Goodwin said, referring to the start of the free-agency period. "There were just a few legal things to work out. Kevin made it clear that he wanted to be in Oklahoma."
The team did not immediately confirm the deal.
The reigning NBA scoring leader is signed with the Thunder through next season under his original rookie contract, which would pay him about $5 million next year.
Oklahoma City, which is well under the salary cap, could offer Durant more than two times that much, depending on where the cap is set for next season.
Information from ESPN.com's J.A. Adande, ESPN.com NBA writer Marc Stein and The Associated Press was used in this report.