"A young girl and a somewhat older man, one from Pakistan and one from India, one Muslim, the other Hindu; both symbols of what the world needs: more unity. Fraternity between the nations!" Thorbjoern Jagland, chairman of the Norwegian Nobel committee, said at the ceremony in Oslo.
Malala, 17, became a global icon after she was shot and nearly killed by the Taliban in October 2012 for insisting that girls had a right to an education.
Malala has already been honoured with a host of awards, standing ovations and plaudits everywhere from the United Nations to Buckingham Palace.
On the eve of the ceremony, she said she would not rest on her laurels, saying she would like one day to become prime minister in her native Pakistan.
"If I can serve my country best through politics and through becoming a prime minister then I would definitely choose that," she told the BBC.
"I want to serve my country and my dream is that my country becomes a developed country and I see every child get an education."
7,000 Norwegian children
Minutes after Malala received the prize, a man carrying a Mexican flag walked towards her, but was caught by security. His motives were unknown.
Before the ceremony, Malala and Yousafzai met with 7,000 Norwegian children aged between six and 14 in the heart of Oslo.
"You have given me so much energy. It's more than a red bull!" Malala said.
At a press conference in Oslo on Tuesday Malala said that in many parts of the world, children's requirements are infinitely more modest than an "iPad or computer."
"What they are asking for is just a book, just a pen, so why can't we do that?"
Satyarthi, 60, was recognized by the Nobel committee for a 35-year battle to free thousands of children from virtual slave labour.
"I refuse to accept that the world is so poor, when just one week of global military expenditure is enough to bring all of our children into classrooms," he said after receiving the prize.
"I refuse to accept that the shackles of slavery can ever be... stronger than the quest for freedom."
Malala was 15 when a Taliban gunman shot her in the head as she travelled on a school bus in response to her campaign for girls' education.
Although she almost died, she recovered after being flown for extensive surgery in Birmingham, central England.
She has been based in the city with her family ever since, continuing both her education and activism.
The pairing of Malala and Satyarthi had the extra symbolism of linking neighbouring countries that have been in conflict for decades.
After she was named as the winner, Malala said she wanted both states' prime ministers to attend the prize-giving ceremony in Oslo.
"If the prime ministers had come here I would have been very happy," she said. "I would have thought of it as a big opportunity to ask them... to make education their top priority and work on it together because we see the number of children who are out of school and suffering from child labour are mostly in India and Pakistan."
Satyarthi's organisation Bachpan Bachao Andolan (Movement to Save Childhood) prides itself on liberating more than 80,000 children from bonded labour in factories and workshops across India and has networks of activists in more than 100 countries.
According to the International Labour Organisation (ILO) there are about 168 million child labourers around the world.
Nobel winners receive eight million Swedish kronor ($1.1 million, €862,000), which is shared in the case of joint wins.
The Peace Prize is the only Nobel award handed to recipients in Oslo.
The other prizes -- also featuring the literature prize winner, Frenchman Patrick Modiano, and his compatriot Jean Tirole with the economics award -- will be awarded in Stockholm later Wednesday.