Rizzo, who won his third Gold Glove on Sunday, agreed in 2013 to a $41 million, seven-year contract that included two club options. He would have received a $2 million buyout if the option had been declined.
Chicago's option for 2021 also is for $16.5 million with a $2 million buyout. If that is exercised, the deal would be worth $72 million over nine seasons.
Morrow's option was for $12 million, and he will receive a $3 million buyout. Barnett and Graveman both had options for $3 million.
Rizzo hit .293 with 27 homers and 94 RBIs this year, ending a streak of four 100-RBI seasons. He finished among the top four in NL MVP voting in 2015 and 2016.
On Saturday, the Cubs exercised their $11.5 million option for 2020 on left-hander José Quintana and declined their $6.5 million option on lefty Derek Holland, which triggered a $500,000 buyout. In addition, pitcher Yu Darvish and outfielder Jason Heyward declined to exercise the opt-out provisions in their contracts, deciding the remain with the Cubs.
Darvish is owed $81 million over the final four seasons of a $126 million, six-year deal, and Heyward is due $86 million in the next four seasons of a $184 million, eight-year contract.
Morrow, 35, agreed to a $21 million, two-year contract before the 2018 season and had 22 saves and a 1.47 ERA in 35 games when he was shut down that July because of a bone bruise in his right elbow. He had elbow surgery last Nov. 6 but has not pitched since.
Barnette, 35, signed a $750,000, one-year contract with the Cubs last winter, a deal that called for an increase to $1 million when he spent one day on the big league active roster. He started the season on the injured list with right elbow tightness and after appearing in 12 games for Triple-A Iowa, he pitched twice for Chicago and was optioned back to Triple-A to open a roster spot for Craig Kimbrel. Barnett didn't report and was placed on the restricted list for the rest of the season.
Graveman, 28, had Tommy John surgery on July 24, 2018, and became a free agent when Oakland failed to offer a 2019 contract. He signed a $575,000, one-year contract with the Cubs and made a pair of three-inning minor league injury rehabilitation appearances, on Aug. 22 for the Arizona League Cubs and for Iowa on Sept. 1.