Federation general manager Eduardo Najri said the choice was made official Thursday and Calipari posted on his website that he has formally accepted the head coaching position.
"This will be a great learning experience for me to be able to coach against some of the best minds in international basketball. I know that being in the NBA helped me do a better job of preparing our young men to reach their dreams and this opportunity will do the same," Calipari said.
The Dominican Republic has never qualified for the Olympics in men's basketball.
Calipari says he would spend about six weeks with the team from August through mid-September, preparing it for the Tournament of the Americas. The team would practice at Kentucky's Joe Craft Center before the tournament, which will be held in Brazil.
The 2009 team that competed in the FIBA Americas championships included Atlanta forward Al Horford and Sacramento swingman Francisco Garcia. The team finished fifth in the tournament with a 4-4 record.
Calipari says he would also help train Dominican coaches. He has a similar relationship with coaches in China.
Louisville coach Rick Pitino had been scheduled to coach the Puerto Rican national team in the same tournament. Pitino, citing scheduling conflicts, changed his plans.
Former Arkansas coach Nolan Richardson unsuccessfully tried to get Mexico into the 2008 Olympics, and longtime NBA coach Del Harris led China to an eighth-place finish in the 2004 Olympics.
Based on reporting by The Associated Press.