Daimler and Rolls-Royce "intend to launch a public tender offer for 100 percent of the share capital of Tognum," a statement, adding that they would offer €24 ($33.36) per share.
That put the total value of the offer at "approximately €3.2 billion," the statement added.
"The public tender offer is intended to be carried out by a 50:50 joint venture company," it said.
Tognum is based in Friedrichshafen, southern Germany, and is a major supplier of engines to Daimler, the world's biggest heavy truck maker.
Daimler already owns 28 percent of the company, which it will tender to the offer.
Daimler and Rolls-Royce want to put Tognum in a strong position to to offer a wider range of products, systems and services, they said. At present, Tognum also builds motors for armoured vehicles and boats and posted sales of €2.5 billion ($3.5 billion) in 2009, a level it expected to reach again in 2010.
Rolls-Royce is to bring its Bergen gas and diesel engine business to the deal along with its "world leading capability in integrated power systems and services," the statement said.
It will also contribute "a well established market presence in the marine, energy and defence sectors."
Daimler meanwhile is well positioned in engine technology and manufacturing expertise and also offers "exceptional access to global markets.
"It is an exciting proposition for Daimler to partner with Rolls-Royce to further invest in the Tognum business," Daimler chairman Dieter Zetsche said in the statement.
Daimler shares showed a gain of 1.66 percent to €50.07 in midday trading on the Frankfurt stock exchange while the DAX index was 0.12 percent higher overall.
Tognum was up by 7.93 percent at €25.05, while the MDax index on which it is listed was 1.22 percent higher.
In London, Rolls-Royce was up 2.50 percent at 615.5 pence while the FTSE-100 index was 0.33 percent lower.