Malala Yousafzai arrived at Birmingham's Queen Elizabeth Hospital where her condition was to be assessed, The Guardian reported. Her recovery could take months.
"Doctors ... believe she has a chance of making a good recovery on every level," said Dr. Dave Rosser, the hospital's medical director.
Malala made the trip to Britain by herself, but her family may follow later, the newspaper said.
"Malala's bravery in standing up for the right of all young girls in Pakistan to an education is an example to us all," British Foreign Secretary William Hague said.
A Pakistani military spokesman said she would need "prolonged care to fully recover from the physical and psychological effects of the trauma that she has received." Her treatment is likely to include the partial rebuilding of her skull and "intensive neuro-rehabilitation."
The girl has been fighting for life since she was shot a week ago. Doctors in Pakistan removed a bullet from her brain.
Malala, who has won worldwide admiration for opposing the Pakistani Taliban in her hometown of Mingora in the Swat Valley since the age of 11 and openly promoting education for girls, had been reported earlier to be showing signs of improvement at a military hospital in the garrison town Rawalpindi near Islamabad.
But a statement from the military's Inter Services Public Relations unit said she was taken to Britain for further treatment after consultation with her family. All expenses for her care would be paid by the Pakistani government, officials said.
The military said Pakistani doctors, after consulting with international experts, concluded Malala "will require prolonged care to fully recover from the physical and psychological effects of trauma that she has received," the Los Angeles Times reported.
Malala had blogged for the BBC Urdu language service, telling about the atrocities of the Taliban.
The girl was shot as she traveled to school. Two other girls were injured but an updated report on their conditions was not available.
The Pakistani Taliban claimed responsibility for the attack, saying Malala had been advocating secularism. Various reports have said the militant group has vowed to kill her if she survives.
The attack has been widely condemned in Pakistan and other countries. There have been prayer vigils for her and protests condemning her shooting in several Pakistani cities.
The Times quoted Pakistani authorities as saying three brothers were arrested on suspicion of being involved in the shooting. About 100 were rounded up earlier for questioning.
"Investigations are in the very early stage," said Iftikhar Hussain, information minister for Khyber-Pakhtunkhwa province where Swat Valley is located.