Cockrell, 52, was hired as Pentland's assistant last January, and he helped guide the Yankees' offense to 764 runs scored (second in the Majors), 212 homers (fourth), a .421 slugging percentage (fourth) and a .744 OPS (fifth).
Cockrell has also spent time as a hitting coach with the Rockies -- in 2002 and then again in '07, when Colorado won the National League pennant -- before leaving in 2008. He spent two years as the hitting coach for the Mariners in 2009-10, before spending 2011-13 as the roving hitting coordinator for the D-backs. Cockrell was also the starting quarterback at the University of Tennessee for two seasons (1982-83) and helped lead the team to a Citrus Bowl victory in '83.
Last season was the first time the Yankees have used two hitting coaches, and they apparently liked the model.
Thames, 38, recently retired in 2011 after playing parts of 10 seasons in the Majors. He was drafted by the Yankees in the 30th round of the 1996 Draft, but he spent most of his career in Detroit.
During his coaching tenure in the Yankees' organization, Thames has served stints as a hitting coach for Class A Advanced Tampa in 2013, Double-A Trenton in '14 and Triple-A Scranton/Wilkes-Barre in '15. He also spent time with the Major League club this past September.
Jamal Collier is a reporter for MLB.com. Follow him on Twitter at @jamalcollier. This story was not subject to the approval of Major League Baseball or its clubs.