Guillen and the White Sox part ways on Monday with just two games remaining in the regular season. Cora was named interim manager at the time, but will not be with the club for the final two contests after speaking with general manager Ken Williams Tuesday morning.
The Florida Marlins are wildly reported to name Guillen their new manager in the near future, and Cora is expected to join him there.
Cooper was awarded a multi-year contract with the White Sox, who also locked up first-base coach Harold Baines with a long-term deal.
Cooper has been with the White Sox for 24 years, serving the last nine as pitching coach. Baines, who played 22 seasons in the majors, is in his eighth season on Chicago's coaching staff.
The club also announced Mike Gellinger will replace Cora as bench coach for the last two games.