The price was not disclosed, but sources familiar with dossier put it "in the region of €150 million" ($199 million).
ThyssenKrupp, which is active in steel, elevators, submarines and car parts, said it had decided to sell the activities as part of a drive to "optimise" its business portfolios.
The Blohm + Voss group of companies specialises in ship components, ship repair and conversion business, pipe-handling equipment and also the design and manufacture of high-end bespoke mega yachts.
It has annual sales of around €400 million and more than 1,500 employees, mostly in Hamburg.
"The sale is an important step in further focusing the activities of ThyssenKrupp Marine Systems. At the same time, the change of owner will help secure jobs and the future of shipbuilding at the various Blohm + Voss sites," said Hans Christoph Atzpodien, head of ThyssenKrupp Marine Systems.
The deal, which is subject to approval by the competition authorities, is expected to be finalised in the first quarter of 2012.
In its own statement, Star Capital said Blohm + Voss was "one of the great brands in the marine industry".
And its new owner pledged to "commit significant amounts of capital to the business to ensure that it is in a position to take advantage of growth opportunities in the future."
"We are pleased to have acquired a world class German engineering business, one in which we intend to invest by providing a significant capital commitment to drive growth and job creation," said Star Capital chief executive Tony Mallin.