Calderón played 14 seasons in the NBA, spending the 2017-18 campaign in Cleveland as the Cavs made their fourth straight trip to the Finals. The 40-year-old was with the Detroit Pistons in 2018-19.
After retiring, he worked with the National Basketball Players Association as an assistant to NBPA executive director Michele Roberts and a senior management team on union strategy and issues relevant to current players.
With the Cavs, Calderón will assist Koby Altman, the team's newly named president of basketball operations.
"We are thrilled to add someone of José Calderón's background and experience to our front office," said Altman, who received a contract extension this week. "His accomplishments as a basketball player and familiarity with our organization will be invaluable.
"We look forward to his insights and perspective on how we can continue moving this team forward and enhancing our efforts towards sustainable and long-term success here in Cleveland."
The Cavs are 24-18 after winning just 22 games last season. They play in San Antonio on Friday.
Calderón averaged 8.9 points and 5.8 assists in 895 career games. He played on four Olympic teams for Spain, winning two silver medals and a bronze.
He played six pro seasons in Spain before breaking in with Toronto in 2005. He spent eight seasons with the Raptors and also played for the Pistons, Mavericks, Lakers, Knicks and Hawks before signing a one-year deal with Cleveland.