Burnham, who said he had moved into his "dream job" as culture secretary, replaces James Purnell who has taken the work and pensions brief following Peter Hain's resignation.
Liverpool-born Burnham has previous experience at the Department for Culture, Media and Sport (DCMS), having worked as a special adviser during Tony Blair's first term in power, when Chris Smith was culture secretary.
He said it was "a fantastic time" to become culture secretary, "with the thriving cultural and arts sector in the country, preparations for the Olympic Games well under way and of course my family's home city this year is crowned as European City of Culture".
"Anybody who knows me knows that I will put my heart and soul into this job," he added.
Burnham praised Purnell, with whom he once shared a flat. "I would like to pay full tribute to my good friend James Purnell who has made a real impact here and I will be very much picking up where James left off," he said.
The British Hospitality Association (BHA) warmly welcomed the appointment.
"We are delighted that Andy Burnham is returning to the DCMS - when he was political adviser there, Bob [Cotton, BHA chief executive] was tourism adviser," a spokesman said.
"It's good to have someone with knowledge of the industry and we look forward to working with him - and to a period of stability at the top of the DCMS."
Travelodge chief executive Grant Hearn added: "We are disappointed that the DCMS leadership has again changed hands after such a short time but given the outgoing secretary of State's lack of interest in tourism, I am not sure that we will feel a major loss.
"We welcome the return to DCMS of Andy Burnham and are looking forward to early discussions on industry issues. As someone who would have presided over the recent cuts in tourism spend, we are looking forward to helping him understand the real potential of UK tourism."
By Daniel Thomas
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