Saudi women have campaigned for decades to get the driving ban removed.
"In order to change women's participation in the workforce we need them to be able to drive to work", said bin Salman, who is a son of the current king and a brother of the crown prince.
Prince Khaled bin Salman, Saudi Arabia's ambassador to the USA, said: "This is a historic big day in our kingdom", while briefing with reporters.
In September women were allowed to enter a sports stadium for the first time to take part in the country's National Day celebrations.
JACKIE NORTHAM, BYLINE: For years, the ban on women driving was held up as a sign of repression in Saudi Arabia.
But after news broke that the ban was being lifted, ambassador to the US Prince Khaled bin Salman told journalists that it was thought of by the government as a social issue, rather than a religious or cultural one. US State Department spokeswoman Heather Nauert called the move "a great step in the right direction".
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Although no election is due until 2022, it is preparing for Theresa May's Conservative minority government to fall much sooner. McDonnell said he wanted to get this underway quickly in the event Labour is voted in to government.
The country has a bad reputation when it comes to women's rights. Women have fought long and hard in the country for their rights and there have been limited reforms to the outdated laws over the years to reduce the male control over women.
In a desert country and with a land mass ten times the size of the United Kingdom, it's ridiculous that women haven't been allowed the means to transport themselves around until now.
While the victory for women who have endured arrests, threats and exile in campaiging to be allowed behind the wheel should not be downplayed, the long-awaited good news that they can now drive has inevitably come with a dose of sketpicism.
Full length abayas - a long coat worn over other clothes - must be worn by all women in public, although in recent years rules over the colour, decoration and how headscarves are worn have been relaxed.
Auto manufacturers may sense opportunities in Saudi Arabia with an expanded market. In Riyadh, some Saudi women have started showing their faces, a change in the conservative capital where most show only their eyes - if that.
"Preventing a woman from driving a vehicle is today an issue of rights similar to the one that forbade her from receiving an education or having an independent identity", Alwaleed said.