The White Sox said in a statement that Reinsdorf, 89, had reached a "long-term investment agreement that establishes a framework for Ishbia to obtain a future controlling interest in the White Sox."
Under the agreement Ishbia, a billionaire private equity investor, will make capital infusions into the White Sox in 2025 and 2026 that will be used to pay down debt "and support ongoing team operations".
From 2029 to 2033 Reinsdorf will have the option to sell controlling interest in the White Sox to Ishbia. If no deal is completed by then, Ishbia will have the option to take over after the 2034 season.
The team's release emphasized that "there is no assurance that any such future transaction will occur, and in no event will such a transaction take place before 2029".
Until then, Reinsdorf will continue to own and operate the team.
The White Sox said that Ishbia's brother Mat Ishbia, the majority owner of the Suns, and his father Jeff Ishbia will also be "significant investors".
Reinsdorf, who is also the principal owner of the NBA's Chicago Bulls, has been the White Sox chairman since 1981.
Reinsdorf bought the White Sox for some $20 million, and the franchise was valued at $2 billion this year by Forbes in the business journal's annual survey of MLB club values.
"Having the incredible opportunity to own the Chicago White Sox and be part of Major League Baseball for nearly 50 years has been a life-changing experience," Reinsdorf said in a statement.
"I have always expressed my intent to operate the White Sox as long as I am able and remain committed to returning this franchise to the level of on-field success we all expect and desire."
The White Sox have reached the playoffs seven times during Reinsdorf's tenure and won the 2005 World Series but have struggled in recent seasons.