A former major league infielder, Renteria spent the past six years on the Padres' staff and had been their bench coach since 2011. Before that, he coached and managed in the San Diego and Florida Marlins organizations.
Renteria also managed Mexico in the World Baseball Classic in March.
The Cubs are counting on him to get the most out of young players such as shortstop Starlin Castro and first baseman Anthony Rizzo, along with prospects such as Javier Baez, Jorge Soler, Albert Almora and Kris Bryant.
The Cubs were 127-197 under Sveum and finished in last place for the first time in seven years.
They had targeted Girardi, a Peoria, Ill., native and Northwestern product who played for them. But the former catcher signed a four-year contract worth up to $20 million to stay with New York through 2017.
That forced the Cubs to look elsewhere.
Besides Renteria, they interviewed former Mariners and Indians manager Eric Wedge, Rays bench coach Dave Martinez, former Nationals and Indians manager Manny Acta, former Diamond-backs manager A.J. Hinch, and Brad Ausmus, who was hired by the Tigers on Sunday.
They were also interested in talking to Boston bench coach Torey Lovullo. But according to reports, the Red Sox invoked an agreement banning Cubs president Theo Epstein from hiring any of their employees over a three-year period.