The 37-year-old Epstein resigned from the Boston Red Sox on Friday night with a year remaining on his contract as general manager to run a team that has gone 103 years without a World Series championship.
With Epstein at the helm, the Red Sox ended an 86-year World Series championship drought in 2004 and won the title again in 2007.
Cubs fans can only hope he will do the same thing on the North Side. Cubs chairman Tom Ricketts fired GM Jim Hendry in July after another disappointing season.
The teams negotiated for more than a week over compensation the Red Sox would receive for letting Epstein out of his contract. In the end, they decided to put off that issue, saying it would be resolved in the near term.
The Red Sox are expected to announce assistant GM Ben Cherington as Epstein's replacement. Boston, which collapsed in September and missed the playoffs for a second straight year, must also find a new manager to replace Terry Francona.
One of the first chores in Chicago is the future of manager Mike Quade, who led the team to a 71-91 record in his first full season. He has another year left on his deal.
Various reports say the Cubs are also interested in hiring San Diego Padres general manager Jed Hoyer for that position where he would be reunited with Epstein. They worked together in Boston.
Epstein will reportedly receive a five-year deal worth about $18.5 million to overhaul the baseball side of the Cubs' front office.
In a joint statement, the teams said they would hold news conferences on Tuesday with the Cubs introducing Epstein and with the Red Sox announcing his successor -- likely Cherington.
Major League Baseball generally prohibits announcements during the World Series, but Friday is a day off between Games 2 and 3 between the Cardinals and Rangers.
The Cubs and Red Sox said they would not comment until Tuesday, another travel day for the World Series if it goes beyond five games.