There were 147 players who became free agents, a group that includes second baseman Robinson Cano; outfielders Jacoby Ellsbury, Carlos Beltran, Shin-Soo Choo and Curtis Granderson; catcher Brian McCann; and pitchers Roy Halladay, Tim Hudson, Ervin Santana, Matt Garza and Fernando Rodney.
About 30 additional players are eligible to go free in coming days if their 2014 options aren't exercised. Among that group is Yankees captain Derek Jeter, who has a $9.5 million player option.
Teams then have until Monday to make $14.1 million qualifying offers to eligible free agents who were on their rosters when the season began. If a player accepts, he is signed for 2014; if he declines and signs elsewhere, his former team gets amateur draft pick compensation for next June's draft.
Shields ($13.5 million) and Chicago White Sox reliever Matt Lindstrom ($4 million) had their options exercised Thursday, preventing them from becoming free agents.
Acquired last off-season from Tampa Bay, Shields went 13-9 with a 3.15 ERA and an AL-leading 228 2-3 innings.
"I feel good about it. I feel like I pitched well for them last year," Shields said. "I'm just excited to be back and be a Royal and have a good season next year."
Among the players whose options were declined were Cardinals pitcher Jake Westbrook ($1 million buyout instead of $9.5 million salary); Texas first baseman-designated hitter Lance Berkman ($1 million instead of $12 million); Dodgers left-hander Chris Capuano ($1 million instead of $8 million) and second baseman Mark Ellis ($1 million instead of $5.25 million); and Colorado reliever Rafael Betancourt ($250,000 instead of $4.25 million).
Cleveland's Jason Giambi went free, then agreed to a minor league contract with the Indians.
Perez, a two-time All-Star, would have been eligible for salary arbitration.
He spent five seasons with the Indians and while he saved 124 games, Perez often was at the centre of turmoil that overshadowed his pitching. He angered Indians fans last season for saying they didn't support the team like they should, and he rankled Cleveland's front office by criticizing trades and stating the Indians weren't spending enough to win.
"We just finished out team meetings and made the determination that Chris was not a fit on our roster," general manager Chris Antonetti said in announcing Perez's release.
In June, Perez was arrested after drug agents followed a package containing marijuana to his home in Rocky River, Ohio. He and his wife pleaded guilty to a misdemeanour charge.