The deal is expected to be announced Thursday once Upton passes his physical. It would be the biggest free-agent contract of the offseason so far and the largest in Braves history.
Upton, 28, hit .246 with 28 homers, 78 RBIs and 31 stolen bases for Tampa Bay last season.
Upton made his debut with Tampa Bay in 2004. His first full season was 2007, when he hit a career-best .300 with 24 homers and 22 stolen bases.
The speedy outfielder's home run totals have increased in each of the last three seasons, but he has hit below .250 with more than 150 strikeouts in four straight years.
The Rays just gave third baseman Evan Longoria a six-year contract extension worth $100 million, but the team was in the bottom third of the league in payroll last season and was not expected to be able to afford Upton.
Upton will become just the third outfielder 28 or younger (as of Opening Day) to receive a free-agent contract of at least $75 million, according to ESPN Stats & Information. The others were Manny Ramirez in 2000 from the Boston Red Sox (eight years, $160 million) and Carlos Beltran in 2004 from the New York Mets (seven years, $119 million).
Upton will replace free agent Michael Bourn as the Braves' center fielder and provide a needed right-handed power bat for the lineup.
Bourn was the Braves' leadoff hitter, but Upton is not expected to fill that role. The Braves might shop for a left fielder to hit leadoff, with Martin Prado expected to move from the outfield to third base following Chipper Jones' retirement.
Young shortstop Andrelton Simmons, who hit .289 with a .335 on-base percentage as a rookie, could be an option to bat leadoff. Prado was the normal No. 2 hitter.
The deal with Upton comes only five days before the start of baseball's winter meetings in Nashville, Tenn.
Upton is an expensive addition, but the big move is not a surprise.
General manager Frank Wren said after the season he would have funds available to make a notable offseason acquisition. Jones had a $14 million base salary last season and Bourn's was $6,845,000.
Wren said he entered the offseason with "a pretty narrow focus" because he only had to replace Bourn and Jones.
"Beyond that, our club is pretty solid," Wren said after the Braves' wild-card playoff loss to St. Louis.
Upton adds to what Wren said is a "dynamic young core" of players. He will join first baseman Freddie Freeman, right fielder Jason Heyward, catcher Brian McCann and second baseman Dan Uggla as power hitters.
McCann's status for the start of the season is uncertain. He had surgery on his right shoulder in October. The rehabilitation could carry into the first month of the season.
Gerald Laird signed a two-year, $3 million deal with Atlanta earlier this month to serve as McCann's backup. Laird, who hit .282 with AL champion Detroit, could open the season as the starter if McCann is not ready.
Upton's agent, Larry Reynolds, did not immediately return messages seeking comment.
Information from ESPN.com's Jerry Crasnick and The Associated Press was used in this report.