The portfolio of 31 themed outlets across the UK, includes 29 Old Orleans-branded properties and two Quincey's-branded operations.
The £26m deal for the Spirit Group‘s managed portfolio is on a cash-free and debt-free basis and is expected to complete in September.
A statement from Regent Inns said the acquisition represented a "significant strategic opportunity" and was in line with the company's drive to seek "value enhancing and consolidation opportunities and, to add a third arm to its portfolio".
Bob Ivell, Regent Inns executive chairman said: "We have previously stated our intention to add further businesses to our portfolio and we believe that the acquisition of Old Orleans will provide a good third platform for future growth and enhance shareholder value."
The Old Orleans brand will now sit alongside Regent Inn's other brands, which include Aussie bar-chain Walkabout and comedy stores, Jongleurs.
Giles Thorley, Punch Taverns chief executive, said the proceeds from the sale would be used to reduce debt. The disposal forms part of the company's planned disposal of 380 units announced in May.
A transitional service agreement for up to six months has been agreed to facilitate a smooth transition.