Guillen was released from his contract Monday night to pursue other opportunities.
"We certainly cannot thank Ozzie enough for all he has done during his eight seasons as manager of the Chicago White Sox, highlighted by an unforgettable 2005 World Series championship," Reinsdorf said in a release issued by the team following its 4-3 victory over the Toronto Blue Jays.
"I personally appreciate everything he has done for this organization, our fans and the city of Chicago. We shared the greatest moments together and wish him nothing but future success in baseball and in life."
Guillen has been publicly showing interest in going to Florida for several weeks. The teams talked about a trade last winter, but the Marlins balked at the White Sox's request of Logan Morrison at the time.
Guillen has been at odds with White Sox GM Ken Williams for a few years.
Guillen has been asking for the White Sox to extend his contract. It's been reported that the Marlins are willing to give Guillen a $4 million/year deal for four years. His White Sox salary is reportedly $2 million.
Jack McKeon announced his retirement Monday. SI reported several weeks ago McKeon was not going to be asked back as manager but would remain as a consultant.
Guillen had a year remaining on his deal with the White Sox, necessitating the White Sox to let him out of his contract.
Guillen would fill the Marlins' goal of getting a big name to manage as they head into a new stadium. He is a resident of Golden Beach in Miami-Dade County.