The CAA confirmed the failure of the Aberystwyth-based business, which was founded in 2009 by Angeles and Aled Rees, on Thursday (17 March).
The couple met in Argentina; Angeles, who is from Argentina, was finishing her studies as a lawyer, while Aled, who is Welsh, was travelling in Argentina.
They were inspired to launch Tango after arranging for friends and family to travel to Argentina for their wedding.
"For our wedding, 36 Welsh people came to celebrate with us in Argentina, and for our honeymoon, we organised for them all to go to Patagonia to experience the thriving Welsh culture there," they wrote on their website.
Welsh migration to the region started in the 1860s and a community has remained there ever since. The Welsh government estimates there are around 50,000 people living in the Chabut province of Argentina with Welsh ancestry.
They continued: "We felt truly inspired and humbled by the Welsh-Patagonians, who all those years ago never gave up working the barren land, and who – 8,000 miles from home – never gave up on their language and culture, and we wanted our friends to see it for themselves.
"We had such fun organising this holiday that we decided to take the next step – to create a family business combining our love for Welsh-Patagonia, our passion for Wales, our enjoyment of holiday planning, and our Welsh-Argentinian expertise to organise group tours to this incredible part of the world."
The CAA said the company, Atol 10002, ceased traded under the names Teithiau Tango and Tango Tours and websites www.tangotours.co.uk and www.teithiautango.co.uk on Wednesday (16 March).
"We are currently collating information from the company and will update this page as soon as possible," the authority added.
Customers have been advised to await a claim form and not use one from another Atol failure.
