One of Cuba's most distinctive anachronisms – roads full of classic cars from the 1950s – looks set to fade into history following the most sweeping relaxation of vehicle imports since the revolution.

For most of the past half century, Havana's traffic has been jammed with Pontiacs, Studebakers, Oldsmobiles, Chevrolets and Soviet imports as a result of tight domestic controls and US sanctions that made it difficult to buy parts and fuel.

Only officials, doctors and others with government connections or proof of foreign exchange income were allowed to purchase new imported cars. Everyone else had to make do with buying, selling and refitting cars made before Fidel Castro took power in 1959.

But in the latest of a series of economic reforms, the council of ministers headed by his brother – the current president, Raúl Castro – on Friday abolished the need for permission and opened up the car market to all citizens.

The Communist party's official newspaper, Granma, said the new regulations "eliminate existing mechanisms of approval for the purchase of motor vehicles from the state".

The measure was partly designed to overcome public frustration at the old regulations, which gave an unfair economic advantage to those who could buy cars and sell them on the black market, often at four or five times the original price.

Granma said the previous system created "resentment, dissatisfaction and, in not a few cases, led to speculation and enrichment".

In 2011, individuals were allowed to buy new cars provided they had permission from the authorities but with almost no new imports this has led to a waiting list of five years.

That approval process has now been lifted and the price will theoretically be set by the market, but state-run businesses will monopolise new car sales and a hefty tax – of up to 100% – may be levied on new models to fund public transport.

As a result, prices of new cars will be extremely high – by some estimates three or four times what vehicles cost in the US. But with more private businesses, increasing overseas remittances and more wealth for farmers, there is unlikely to be a shortage of demand.

Since Raúl Castro took power in 2008, his government has loosened controls on private enterprise and overseas travel, and announced plans to reduce the public payroll by half a million workers. Thousands of small restaurants and clothes shops have since opened up across Havana, more kiosks are visible along the highways and travellers now have the option of staying in small family-run lodges as well as state-run hotels.

The traffic is also slowly changing. Old US and Soviet cars (often with Japanese engines under the bonnet) are still very visible, but they now line up at lights alongside more modern vehicles, including a new fleet of Chinese-made public buses.