Hyers was the assistant hitting coach for the National League champion Dodgers the last two seasons and also served as the team's director of Minor League hitting in 2017.
With Hyers helping out hitting coach Turner Ward, the Dodgers set franchise records this past season in home runs, doubles and extra-base hits.
Hyers is a strong believer in plate discipline.
This marks a return to the Red Sox for the 46-year-old Hyers, who served as an area scout for Georgia (2009-12) and then as a Minor League hitting instructor in Boston's farm system from 2013-15. In 2014, Hyers spent the final four months of the season on the Red Sox' Major League coaching staff while hitting coach Greg Colbrunn recovered from an injury.
Hyers played in 133 Major League games for the Padres, Tigers and Marlins.
For Barkett, this will be his first stint on a Major League coaching staff after spending 12 seasons as a Minor League coach, including nine as a manager. In 2017, the 43-year-old Barkett managed the Pirates' Triple-A affiliate at Indianapolis. He initially joined the Pirates as an assistant coordinator in 2016 and held that same role with the Marlins in 2015.
Earlier this week, the Red Sox hired Ron Roenicke as bench coach, Tom Goodwin as first-base coach/outfield instructor and Carlos Febles as third-base coach/infield instructor. The club also announced that Dana Levangie is returning as bullpen coach/catching instructor. He will be the only holdover from former manager John Farrell's staff.
Cora, who served as bench coach for the World Series champion Astros, will be formally introduced at a press conference as Boston's new manager on Monday at Fenway Park.
Ian Browne has covered the Red Sox for MLB.com since 2002. Follow him on Twitter @IanMBrowne and Facebook. This story was not subject to the approval of Major League Baseball or its clubs.