They were awarded the prize by the European Parliament in 2005, but Cuba barred them from leaving the communist-run island to collect it.
The abolition of exit permits by the Cuban government in January has made it possible for the women to travel.
They were given the prize for their campaign to free 75 jailed dissidents.
The Sakharov Prize for Freedom of Thought is awarded annually by the European Parliament to individuals or organisations who have dedicated their lives to the defence of human rights and freedom. It is named after the late Soviet dissident Andrei Sakharov.
In 2012, it went to Iranian activists Jafar Panahi and Nasrin Sotoudeh.
The Ladies in White was founded by the wives, sisters and friends of the 75 jailed Cuban activists, who were rounded up and sentenced to long prison terms in 2003 as part of a crackdown on the opposition movement.
Dressed in white, the women march in silence in the Cuban capital, Havana, every Sunday, defying Cuba’s ban on organised opposition and street demonstrations.
They are routinely detained and their protests broken up, but they say their protests have yielded results. All 75 prisoners they campaigned for have been released.
The Ladies continue their protest, now demanding that the convictions of the 75 be officially overturned.
They say that until that happens, the dissidents could be arrested if the government deems they have reoffended.
Fifteen of the 75 remain in Cuba, the rest took up an offer by the Spanish government to move there.
The women also want to draw attention to other dissidents who they say are still jailed for their political views.
Lady in White Laura Labrada told the BBC’s Sarah Rainsford in Havana that they still suffered harassment at the hands of the Cuban police.
“The arrests continue. It’s true the time in detention is less, but we’re still repressed, still detained – and in big numbers. Just for thinking differently… This has not changed,” she said.
The Cuban authorities say that the group is in the pay of the United States and forms part of Washington’s “decades-old effort to undermine Cuba’s socialist revolution”.
Source: BBC World
Ms Labrada will be collecting the prize on behalf of her mother, co-founder of the Ladies in White Laura Pollan, who died in 2011.
She will be joined by three other Ladies in White at the ceremony in the European Parliament in Brussels.
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