The deal is worth up to $30 million, including $18 million over the next two seasons, a source told ESPN NFL Insider Adam Schefter.
"I always wanted to be back in Atlanta,'' White told ESPN.com. "Once we got to the guaranteed money that I wanted to get to that I felt would secure my future as a football player, then I could sign a contract.
"When we got it done, I was happy, because I don't want to go anywhere. I love this place. I wanted to be here. And I'm going to be here for the next four years.''
White said the sides agree to terms at 1 a.m. ET on Thursday morning.
White, who will turn 33 in November, was set to enter the last year of his contract in 2014. The four-time Pro Bowler expected an extension before training camp started on Friday.
Veterans are set to report Thursday afternoon, and White might not have showed without a new contract.
The former first-round pick had six consecutive seasons of 1,000 receiving yards before last season. Hamstring and ankle injuries limited him to 13 games and 711 receiving yards last season, but White picked up his production toward the end of the season.
Since entering the league in 2005, White's 685 receptions rank eighth among active players, while his 9,436 receiving yards rank fifth. His 55 touchdown catches during that time also rank 10th in the NFL.