Bryant, whose name had surfaced in trade rumors this offseason, had a .282 batting average with 31 home runs and 77 RBIs last season. He was eighth in the National League with 108 runs scored and drew enough walks to post a .382 on-base percentage, 16th in the majors.
He missed the final week of the regular season after spraining his right ankle when he landed awkwardly on a wet first-base bag while trying to beat out a double play.
There also is the matter of a service time grievance against the Cubs that was filed on Bryant's behalf by the Major League Baseball Players Association. That grievance is expected to be resolved in the next two weeks, sources told ESPN's Jeff Passan.
Bryant contends he should have started the 2015 season with the big league club, allowing him to become a free agent after the 2020 season. Instead, the Cubs sent him to the minors out of spring training, then brought him up 10 days later because of an injury, allowing them to keep him an extra year and making him a free agent after the 2021 season.
If Bryant wins the grievance, this would be his final arbitration year and he would be a free agent after the 2020 season. If, as expected, he loses, he will have one more arbitration-eligible year and would become a free agent after the 2021 season.
Bryant, selected by the Cubs with the second overall pick in the 2013 MLB draft, was the NL Rookie of the Year in 2015 and the NL Most Valuable Player in 2016.
The Cubs also reached one-year agreements Friday with shortstop Javier Baez, catcher Willson Contreras ($4.5 million), left fielder Kyle Schwarber ($7.01 million) and center fielder Albert Almora Jr. ($1.575 million).
Baez, one of baseball's most exciting players, nearly doubled his salary from $5.2 million last season. He hit .281 with 29 homers and made his second consecutive All-Star team after finishing second to Milwaukee's Christian Yelich in the 2018 NL MVP voting. Baez is under contractual control for two more years and could be in for a contract extension.
Contreras made his second straight All-Star team last season, hitting .272 with a career-high 24 homers and 64 RBIs. Like Bryant, Contreras could be traded to stock up on young players.
Schwarber, who made $3.39 million, set career highs with a .250 average, 38 homers and 92 RBIs. He was particularly good after the All-Star break, hitting .280 and going deep 20 times while driving in 49 runs.
The Cubs hope Almora can rebound after his batting average dropped 50 points to .236 and his on-base percentage fell from .323 to .271. The former first-round pick hit just .213 against left-handers even though he is a righty. And his average on balls in play dropped from .337 in 2018 to .255.
Chicago missed the playoffs for the first time since 2014 after finishing 84-78. The Cubs hired former catcher David Ross to replace Joe Maddon as manager, hoping "Grandpa Rossy" could give them a spark.
The Associated Press contributed to this report.