Cora, 44, who served as the Astros' bench coach in 2017, was specifically named in the Commissioner's report as the person who spearheaded the operation to use stolen sign information from the team's replay to gain a competitive edge.
The Red Sox organization released a statement on Twitter.
"Today we met to discuss the Commissioner's report related to the Houston Astros investigation," the organization said. "Given the findings and the Commissioner's ruling, we collectively decided that it would not be possible for Alex to effectively lead the club going forward and we mutually agreed to part ways."
Cora also commented on the Red Sox decision to part ways.
"We agreed today that parting ways was the best thing for the organization. I do not want to be a distraction to the Red Sox as they move forward," Cora said. "My two years as manager were the best years of my life. It was an honor to manage these teams and help bring a World Series Championship back to Boston."
Cora is the first individual outside the Astros' organization affected by the Commissioner's findings.
Astros' general manager Jeff Lunhow and manager A.J. Hinch both received a one-year suspension for their part in the team's illegal use of technology to steal signs.