Alan Hudson, Craig Lewis and Joe O'Connor of Ernst & Young were appointed joint administrators of Dreams and immediately sold its business and assets to a new company controlled by Sun Capital Partners.
In total, the business had 266 stores across the UK and about 2,000 employees. A total of 171 stores were included in the sale and the administrators said they were seeking buyers for the remaining stores, which will remain open for business.
In Wales, two stores in Cardiff as well as stores in Bridgend, Caerphilly, Cwmbran, Llantrisant, Llandudno, Merthyr Tydfil, Newport, Port Talbot and Swansea have been sold.
But stores in Carmarthen, Llanelli and one in Cardiff are among the 95 not included in the sale.
Hudson said: "High street retailers have faced unprecedented conditions over recent years, and the market for higher value discretionary purchases has been particularly tough.
"Dreams is a well known market leader, but in common with many others has suffered as a result of this depressed retail environment, a rapid expansion of its store portfolio and onerous lease liabilities.
"While recent performance has improved, it has seen a decline in like for like sales across its store portfolio as well as its operating margins being squeezed. This has resulted in the business being unable to continue to operate outside of administration."
Dreams, which is headquartered in High Wycombe, dates back to 1985 with the opening of a sofa bed shop in Uxbridge.