For a man whose estimated wealth tops £32bn, the telecoms tycoon Carlos Slim is famous for living rather modestly. But there was nothing self-effacing about the inauguration of the new museum built to house his vast art collection.

The 1,500 guests who filled the vast atrium were a who's who of Mexico's business, cultural and political elite. The lineup at the ceremonial cutting of the ribbon was particularly eclectic.

To Slim's left was Mexico's conservative president, Felipe Calderón, Colombia's celebrated novelist Gabriel García Márquez, and British financier Sir Evelyn de Rothschild. To his right was Larry King, sporting his trademark braces.

All of them used their own individual scissors to cut the ribbon and open the 6,800 sq metres of exhibition space that is mostly filled with works from Slim's 66,000-piece collection.

Aside from the obligatory inclusion of paintings and murals by great post-revolutionary Mexican artists such as Diego Rivera and Rufino Tamayo, the collection is dominated by European masters. Artists featured include Tintoretto, Murillo, El Greco, Rubens, Monet, Renoir, Van Gogh, Matisse, Dali and Miro. The highlight is the biggest collection of Rodin sculptures outside of France. It all adds up, according to King, to "one of the best art museums in the world".

The Soumaya Museum is named after Slim's wife, with whom he had six children and started his art collection, but who died in 1999 of kidney failure. The collection had been housed in another smaller museum in the south of Mexico City which will remain open.

The new building is part of a major £490m new development called Plaza Carso on the edge of the business district of Polanco that includes apartment blocks, a five-star hotel and malls filled with branches of Slim-owned companies.

True to his habit of putting family members in key positions within his empire, the new museum was designed by his son-in-law, Fernando Romero, a young Mexican architect who had never done anything on this scale before.

Shaped rather like a twisted cube that has been hit by several waves from different angles and covered by 16,000 shimmering aluminium hexagons, from the outside it is somewhat reminiscent of the Guggenheim in Bilbao, Spain. Inside, the use of sweeping ramps, as well as escalators and stairs, conjure up elements of the Guggenheim in New York.

Slim himself described it as "a high world class quality museum", and pronounced himself "proud to be able to offer this building and this collection to the city and the people of Mexico".

Entrance to the museum would, the magnate promised, be free now and forever more. He added that one of his motivations for concentrating on collecting works by European masters was to provide Mexicans who cannot afford to travel with an experience that would otherwise be impossible.

Slim made his fortune in telecommunications. He also controls a wide range of retail shops, as well as infrastructure, mining and drilling companies.

Over the last few years Slim, now 71, has stepped back from the day-to-day running of his businesses, handing most of it over to various members of his family.

He has also stepped up his donations to charity, particularly in health and education. This has partially silenced the critics who claim he became the richest man in the world because Bill Gates and Warren Buffett had given so much of their money away.

Although he tends to be rather discreet in his public pronouncements, Slim is viewed as a major power behind the scenes in Mexico, which is one of the reasons why the inauguration was full with domestic political figures.

Even Larry King got drawn into the political undercurrents after he gushed that Mexico was "a fabulous country" to which tourists were bound to flock once they found out about the museum.

President Calderón immediately pounced on the opportunity to complain about the general pessimism currently enveloping much of Mexico as a result of the country's bloody drug wars.

"Thank you for your comments about our country, Mr King," he said. "Yes, Mexico is a great country, but what is most important is that Mexicans [start to] realise this themselves."

From Rubens to Rivera

Carlos Slim's art collection is primarily focused on European art from the 15th to the 20th century.

The most valuable piece is believed to be a painting from Leonardo da Vinci's studio, Madonna dei Fusi (Madonna of the Yarnwinder).

There are also works accredited to Tintoretto, Murillo, El Greco and Rubens, as well as a substantial number of Impressionist paintings by the likes of Monet, Cezanne, Degas and Van Gogh and a number of more modern pieces from Dali, Picasso and Miro.

The numerical and sentimental core of the collection is made up of sculptures by Auguste Rodin, the biggest outside France and a particular favourite of Slim's wife before she died.

Mexico's post-revolutionary art boom is also represented with works by Diego Rivera and his contemporaries, and a mural called Still Life by the more modern Rufino Tamayo that will be displayed permanently in the museum's entrance alongside a copy of Rodin's The Thinker.

Slim also owns an important number of colonial coins and documents including letters from Spanish conquistador Hernán Cortés.

• This article was amended on 3 March 2011. The original said that Slim tends to be rather discrete in his public pronouncements. This has been corrected.