The Nobel committee described both laureates as “champions of peace”.
The Pakistani education activist said she was there to stand up for the rights of forgotten and frightened children, and raise their voice rather than pity them.
Kailash Satyarthi said receiving the prize was “a great opportunity” to further his work against child slavery.
Malala Yousafzai and Kailash Satyarthi received their awards from the chairman of the Norwegian Nobel committee, in the presence of King Harald V of Norway.
They delivered their Nobel lectures during the award ceremony.
In her speech, Malala Yousafzai, 17, said the award was not just for her: “It is for those forgotten children who want education. It is for those frightened children who want peace. It is for those voiceless children who want change.
“I am here to stand up for their rights, raise their voice. It is not time to pity them. It is time to take action so it becomes the last time that we see a child deprived of education.”
Malala Yousafzai was shot in the head by Taliban gunmen in October 2012 for campaigning for girls’ education and now lives in the UK.
She is the youngest-ever recipient of a Nobel Prize.
She said she had brought other girls with her to Oslo with similar stories, among them two classmates shot alongside her by the Taliban.
Malala Yousafzai said she was dedicating the prize money to the Malala Fund, “to help give girls everywhere a quality education and call on leaders to help girls like me…”
“I will continue this fight until I see every child in school,” she added.
“I feel much stronger after the attack that I endured, because I know, no-one can stop me, or stop us, because now we are millions, standing up together.”
In his speech earlier, Kailash Satyarthi, 60, said he was “representing the sound of silence” and the “millions of those children who are left behind”.
He said he had kept an empty chair at the ceremony as a reminder of the children without a voice.
“There is no greater violence than to deny the dreams of our children,” he said.
“I refuse to accept that the shackles of slavery can ever be stronger than the quest for freedom,” he added, to applause.
Nobel committee chairman Thorbjorn Jagland stressed the importance of education, saying: “The road to democracy and freedom is paved with knowledge.”
Thorbjorn Jagland praised Kailash Satyarthi’s work campaigning against child labor, often at great risk to himself.
He also lauded Malala Yousafzai’s efforts to promote education despite threats from the Taliban, saying: “Her courage is almost indescribable.”
Indian and Pakistani leaders congratulated the laureates.
Malala Yousafzai and Kailash Satyarthi were jointly awarded the 2014 Nobel Peace Prize “for their struggle against the suppression of children and young people and for the right of all children to education”.
Malala Yousafzai and Kailash Satyarthi have split the $1.4 million prize money.
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