The exact date remains uncertain because lawyers on both sides are "crossing all of the T's and dotting all of the I's," which could take a little longer than expected, The Detroit Free Press reported.
A celebration is tentatively planned for Aug. 1, it said.
DaimlerChrysler and Cerberus representatives declined to comment.
Meanwhile, signs at Chrysler's Auburn Hills, Mich., headquarters are already being changed, the newspaper said. "Daimler" was recently removed from an external granite sign at Chrysler's Technical Center building, for example.
The new owners plan to change the signs at Chrysler's 30 North American production facilities over time, rather than right away, to save money, manufacturing Executive Vice President Frank Ewasyshyn said.
"There is a lot of signage. They're not cheap," he said.