The investment group, which also owns furniture chain ScS sofas, beat off rival bidders including Dreams founder Mike Clare and Sir Philip Green, to rescue around two-thirds of stores in a pre-packaged administration deal worth around £35m.
However, a further 350 jobs remain at risk while administrators Ernst and Young continue to seek a buyer for the 93 stores excluded from the Sun European Deal.
Mr Clare, whose own takeover bid was defeated, said he is devising a plan to rescue "as many" of the remaining stores, and jobs, as possible.
Sun European, which also acquired Dreams' High Wycombe head office and two factories, said it was confident the slimmed down business would thrive.
"Dreams is a well-recognised brand known for its wide product range of beds, headboards, mattresses and associated products," said Jordan Wadsworth, vice president of Sun European Partners.
"Despite operating with an over-expanded store base and significant debt in the precarious economic climate of recent years, the business remains the market leader and, with our support, is now well positioned to capitalise on future opportunities.”
Dreams was put up for sale by owner Exponent (NasdaqGS: EXPO - news) earlier this year after its main lender, RBS (LSE: RBS.L - news) , piled on pressure for a funding injection . The retailer, which dominates the British beds market, has been hit by a slowdown in consumer spending in recent years.
It called in the administrators late on Tuesday, immediately before Sun European made the acquisition.