The supervisory board "approved the concept for the Chrysler Group and the realignment of DaimlerChrysler AG in the form submitted by the board of management," DaimlerChrysler said in a statement.
"The closing of the transaction is expected to take place in the third quarter," the statement added.
The statement from the Stuttgart, Germany, company provided no further details and said no more about the board meeting.
DaimlerChrysler said Monday it would sell control of Chrysler to Cerberus for $7.4 billion.
The sale, backed by the United Autoworkers Union, leaves DaimlerChrysler with a 19.9 percent stake in the Auburn Hills, Mich., automaker, to be known as Chrysler Holding LLC.
DaimlerChrysler will change its name to Daimler AG.
Of the $7.4 billion, Cerberus agreed to invest $5 billion in the new Chrysler and $1.05 billion in Chrysler's financial arm. The remaining $1.35 billion will go to DaimlerChrysler, the companies said.
Daimler-Benz AG paid $36 billion for Chrysler in 1998.