Western governments and activists have urged China to release the 57-year-old, who has never been charged with a crime.
Liu Hui, Ms Liu's younger brother, told Radio Television Hong Kong they were informed she was able to leave Beijing last week and that he was happy to send his sister off.
Almost eight years ago, neither Liu nor her husband's supporters foresaw the repercussions the award would have on her: a writer and artist who never considered herself a political person.
Liu's release comes as Chinese Premier Li Keqiang is visiting Germany, a country that in May said it would welcome the widow after a recording was released of her crying in desperation and indicating she had lost hope of being able to leave China.
"Liu Xia never gave up on her wrongfully imprisoned late husband, and for this she was cruelly punished". However, after eight years under illegal house arrest her health is a cause for genuine concern.
Croatian players' kids delight World Cup fans with post-win scratch match
All credit goes to prolific goalscorer Mario Mandzukic for scoring the goal in the second period of extra-time. The teams then traded two scores each before Ivan Rakitic calmly converted the winning penalty.
"Liu Xia was never a political person, and yet, for nearly eight years enormous misery was heaped upon her by Chinese authorities for the crime of merely having married her husband", Genser said in a statement Tuesday.
Liu Xiaobo was jailed for 11 years in 2009 on subversion charges after co-authoring a petition known as Charter 08 calling for sweeping political reforms in China.
In a July 2017 photo released by the Shenyang Municipal Information Office, Liu Xia, wife of jailed Nobel Peace Prize victor and Chinese dissident Liu Xiaobo, holds a portrait of him during his funeral at a funeral parlor in Shenyang in northeastern China's Liaoning Province. State security assigned guards around-the-clock outside her Beijing home and restricted her access to the internet and the outside world, allowing her only occasional phone calls with a small circle of friends. In a May visit to Beijing, German Chancellor Angela Merkel pressed the Chinese leadership on its human rights record and raised Liu Xia's case directly with China's leader Xi Jinping.
Hua Chunying, a Chinese foreign ministry spokeswoman, said Liu's travel to Germany for medical treatment was "of her own free will". "The German government deserves credit for its sustained pressure and hard work to gain Liu Xia's release".
Liu Xia is an accomplished artist and poet who reluctantly followed her husband into politics two decades ago.
Others said Beijing might be trying to curry favour with Western powers ahead of an EU-China summit next week, as both Europe and China fight trade battles with the United States.
England and Belgium to win
It is in the knockout rounds that I hit my stride, though, and I hope to continue like this. It was hard to take two years ago, and we do not want a repeat of that".
Amnesty International reported that Liu told a friend in Germany in April, "If I can't leave, I'll die in my home".
Close friend Ye Du, speaking to AFP before Liu's departure, said she was suffering from "very severe" depression, adding she would "sometimes faint" and was taking medicine to sleep.
Liu Xiaobo died of liver cancer last July while under government custody, prompting a new round of worldwide calls for his widow's release.
But he said great anger remained among Liu Xia's supporters and rights campaigners.
And Zeid Ra'ad Al Hussein, the United Nations High Commissioner for Human Rights, welcomed the development, but called on Beijing to allow Liu Hui to follow her.
"It's easier to die than live".
Roger Federer stopped in Wimbledon quarterfinals by South African Kevin Anderson
The eight-time champion and 20-time grand slam victor last played a Wimbledon match outside Centre Court in 2015. South African Kevin Anderson outlasted Roger Federer 13-11 in the fifth set of their Wimbledon quarterfinal.
The Chinese foreign ministry confirmed Liu Xia's departure, according to AP. "Using death to defy could not be any simpler for me". The last time China let a high-profile political prisoner leave was in 2012, when blind activist Chen Guangcheng was allowed to fly to NY after escaping from house arrest and hiding for six days in the U.S. Embassy in Beijing. He said China's constitution protected human rights.