"In consideration of cash, cash equivalents, debts and pensions, DaimlerChrysler will benefit from a cash inflow of an estimated 1.0 billion euros," Daimler said in a statement.
It said it expected the sale to boost operating profit by 0.4 billion euros and net profit by 0.3 billion euros, but gave no time period.
The deal would close in the first quarter of 2006, it said.
The divestment is seen as a key part of Daimler's plans to finance planned job reductions via voluntary redundancies - costing 950 million euros - at its Mercedes Car Group division in Germany, where it wants to cut up to 8,500 jobs.
Sources close to the transaction had told Reuters that the unit would be sold to EQT.
Kohlberg Kravis Roberts and Dubai International Capital had been the early front runners to buy the business for about 1.7 billion euros.
German truckmaker MAN was also a finalist in the sales process and was the favourite of MTU staff who feared a financial buyer would break up MTU.
MTU makes engines for ships, locomotives, power plants, heavy vehicles and tanks. It had sales of 1.35 billion euros in 2004.
The head of EQT's German business told Reuters there were currently no plans for job cuts or plant closures.
The group of businesses being sold includes heavy diesel engine business MTU Friedrichshafen as well as Detroit Diesel's off-highway unit.