The Norwegian Nobel Committee said that the two laureates had "made a crucial contribution to focusing attention on, and combating, such war crimes".
Iraqi state television interrupted its schedule for a special broadcast about Ms Murad's award of the Nobel Prize, hailing her as the first Iraqi citizen to win the international accolade. Iraq's newly elected President Barham Salih congratulated Ms Murad, saying her award was international recognition of the "catastrophe" that Yazidis were subject to by ISIS.
Mr Mukwege said he heard that he was the co-winner while he was at the operating table and said the news was “touching”.
Mr Mukwege is a Congolese gynaecologist who founded the Panzi Hospital where he specialises in treating women who have been victims of gang rape.
Mr Mukwege is the world's leading expert in surgery following sexual assault and has treated thousands of women. He treats up to 10 patients in theatre daily, often working 18-hour days.
In 2012 Mr Mukwege gave a speech to the UN and in 2014 he was awarded the European Union's highest human rights accolade, the Sakharov Prize for Freedom of Thought.
This is what the Nobel committee said:
Ms Murad is a Yazidi activist who survived her kidnapping by ISIS in 2014. She campaigns for victims of human trafficking and refugees.
Ms Murad has worked with the United Nations, human rights lawyer Amal Clooney and Pope Francis on helping Yazidis who are still in captivity and highlighting the challenges religious minorities face in Iraq and Syria.
The Nobel committee said:
In August she announced her engagement to a fellow human-rights activist, four years after escaping ISIS.
This year's winners will be invited to attend a formal award ceremony at Oslo's City Hall on December 10.
Aside from the winners, the Syrian civilian aid group, the White Helmets, Russia's Novaya Gazeta newspaper, Edward Snowden and Filippo Grandi, the UN High Commissioner for Refugees were among the nominees this year.
Last year's winner was the International Campaign to Abolish Nuclear Weapons.
Winners are chosen by a five-member panel selected from the Storting, Norway's parliament.
The Peace Prize is awarded in Oslo, not in Stockholm, the Sweden, where Alfred Nobel was born and where the Nobel Prizes in Physics, Chemistry, Physiology or Medicine, Literature and the Economics Prize are being awarded this week.
The Oslo committee received nominations for 216 individuals and 115 organisations. Candidates can be nominated by heads of state, government ministers, senior academics and previous peace prize winners.
The prestigeous prize has not been without controversy over the years, most recently when the former US President Barack Obama won in 2009 after less than a year in office.
The following is the full text of the Nobel Peace Prize award for 2018.
The Nobel Committee's statement
The Norwegian Nobel Committee has decided to award the Nobel Peace Prize for 2018 to Denis Mukwege and Nadia Murad for their efforts to end the use of sexual violence as a weapon of war and armed conflict. Both laureates have made a crucial contribution to focusing attention on, and combating, such war crimes.
Denis Mukwege is the helper who has devoted his life to defending these victims. Nadia Murad is the witness who tells of the abuses perpetrated against herself and others. Each of them in their own way has helped to give greater visibility to war-time sexual violence, so that the perpetrators can be held accountable for their actions.
The physician Denis Mukwege has spent large parts of his adult life helping the victims of sexual violence in the Democratic Republic of Congo. Since the Panzi Hospital was established in Bukavu in 2008, Dr Mukwege and his staff have treated thousands of patients who have fallen victim to such assaults. Most of the abuses have been committed in the context of a long-lasting civil war that has cost the lives of more than six million Congolese.
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Denis Mukwege is the foremost, most unifying symbol, both nationally and internationally, of the struggle to end sexual violence in war and armed conflicts. His basic principle is that "justice is everyone's business". Men and women, officers and soldiers, and local, national and international authorities alike all have a shared responsibility for reporting, and combating, this type of war crime.
The importance of Dr Mukwege’s enduring, dedicated and selfless efforts in this field cannot be overstated. He has repeatedly condemned impunity for mass rape and criticised the Congolese government and other countries for not doing enough to stop the use of sexual violence against women as a strategy and weapon of war.
Nadia Murad is herself a victim of war crimes. She refused to accept the social codes that require women to remain silent and ashamed of the abuses to which they have been subjected. She has shown uncommon courage in recounting her own sufferings and speaking up on behalf of other victims.
Nadia Murad is a member of the Yazidi minority in northern Iraq, where she lived with her family in the remote village of Kocho. In August 2014 the Islamic State [ISIS] launched a brutal, systematic attack on the villages of the Sinjar district, aimed at exterminating the Yazidi population.
In Nadia Murad’s village, several hundred people were massacred. The younger women, including underage children, were abducted and held as sex slaves. While a captive of the IS, Nadia Murad was repeatedly subjected to rape and other abuses. Her assaulters threatened to execute her if she did not convert to their hateful, inhuman version of Islam.
Nadia Murad is just one of an estimated 3,000 Yazidi girls and women who were victims of rape and other abuses by the IS army. The abuses were systematic, and part of a military strategy. Thus they served as a weapon in the fight against Yazidis and other religious minorities.
After a three-month nightmare Nadia Murad managed to flee. Following her escape, she chose to speak openly about what she had suffered. In 2016, at the age of just 23, she was named the UN's first Goodwill Ambassador for the Dignity of Survivors of Human Trafficking.
This year marks a decade since the UN Security Council adopted Resolution 1820 (2008), which determined that the use of sexual violence as a weapon of war and armed conflict constitutes both a war crime and a threat to international peace and security. This is also set out in the Rome Statute of 1998, which governs the work of the International Criminal Court.
The Statute establishes that sexual violence in war and armed conflict is a grave violation of international law. A more peaceful world can only be achieved if women and their fundamental rights and security are recognised and protected in war.
This year's Nobel Peace Prize is firmly embedded in the criteria spelled out in Alfred Nobel's will. Denis Mukwege and Nadia Murad have both put their personal security at risk by courageously combating war crimes and seeking justice for the victims. They have thereby promoted the fraternity of nations through the application of principles of international law.
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