The deal is worth $132 million, sources told ESPN's Jeff Passan.
The deal, which was first reported Sunday as being close by Boston radio station WEEI, includes the $12 million the 26-year-old Bogaerts was scheduled to make this season, then $120 million over the final six years.
The deal, according to sources, will include an opt-out clause that Bogaerts can exercise following the 2022 season, when he will be 30 years old.
There also is a team vesting option for 2026, worth another $20 million, the sources said.
Bogaerts hit .288 last year and set career bests with 23 homers and 103 RBIs while helping the Red Sox win a franchise-record 108 games in the regular season and a World Series championship. The native of Aruba finished 13th in American League MVP voting.
Bogaerts has played all six-plus seasons in his major leagues with the Red Sox after making his debut in 2013. He has 75 career home runs, 834 hits and 387 RBIs and has appeared in the postseason four times.
Bogaerts, who has won two World Series rings with the Red Sox, said his closeness with his teammates and faith in the organization made Boston the right fit for him.
"It's a very special place to play," Bogaerts said. "The fans, the organization in general, expect winning, and I know my teammates know how much I love winning ... whether it's cards, baseball, dominoes, I don't care."
Bogaerts is well liked in the locker room, and many of his teammates crowded the back of the room for the news conference in Oakland, California, including Chris Sale, Mookie Betts, Jackie Bradley Jr., Rafael Devers, Mitch Moreland, Christian Vazquez, Matt Barnes, Brian Johnson, Brock Holt and others.
"I'm blessed to have teammates like that, and the coaching staff. ... The group we had last year and the guys we have this year, it goes beyond regular guys, it's a real family," Bogaerts said.
It's the second time in eight days that the team has made a big commitment to a player who helped it win a third consecutive AL East title and fourth World Series since the beginning of 2004. Sale signed a $145 million extension for five years on March 22.
Betts, the reigning AL MVP, is eligible for salary arbitration after this season and for free agency after 2020, when he will be just 28. He will earn $20 million this year.
The Associated Press contributed to this report.