The status for the rest of the staff is not known. First-base coach Dave McKay, hitting coach Dave Magadan and pitching coach Mike Butcher have one year remaining on their contracts, while bench coach Glenn Sherlock and bullpen coach Garvin Alston had deals that expired Oct. 31.
• D-backs introduce Lovullo as manager
Williams was an original D-back, acquired after the Expansion Draft in 1997. He played from 1998-03 with Arizona before retiring.
Following retirement, Williams bought a small ownership stake in the team and worked in various capacities with the organization. In 2010, he joined the Major League coaching staff where he remained until being named manager of the Nationals in 2014.
After being dismissed by the Nationals at the end of the 2015 season, Williams returned to the D-backs as third-base coach.
Grace signed as a free agent with the D-backs in 2001 and played for three seasons before retiring. He became the team's analyst on television broadcasts where he remained until being suspended in 2012.
After spending the 2013 and '14 seasons coaching in the lowest rungs of the D-backs' farm system, Grace was named assistant hitting coach in '15.
Both Williams and Grace were members of the 2001 D-backs World Series championship team, and their likenesses are part of an in-game "Legends Race" promotion.
Steve Gilbert has covered the D-backs for MLB.com since 2001. Follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.