Jesse Leroy Matthew Jr, 32, has been charged with abduction with intent to defile Ms Graham, who has been missing since 13 September.
Thousands of volunteers had joined searches for the student, who was born in the UK but has lived in the US since she was five
Virginia State Police have said Matthew's arrest provided a "forensic link" to the 2009 unsolved murder of Morgan Harrington, a 20-year-old who also went missing from Charlottesville.
More follows...rollercoaster"
Continue reading the main story
Related Stories
'Nobody knows where my brother is' Watch
Nepal disaster toll rises to 39
Himalaya trekkers 'herded to deaths'
Relatives of Britons missing in Nepal after snowstorms hit have spoken of their relief that some have made contact to say they are safe.
Amanda Vardy said she had received the good news in an email from a tour company her brother, Nigel, was with.
Christopher Kneale, father of Clare Glazebrook, said he had also heard that his daughter's group was safe.
Others, who had been on trekking holidays, remain missing and a Facebook page has been set up to help find them.
At least 39 people have died in the storms and 150 have been injured, the Nepali authorities have said.
Ms Vardy had previously spoken of her concern for her brother who had been in "constant contact with the family" before communications suddenly stopped.
But she said she had now received an email which read: "All our team are fine and secure.
"They safely reached base camp. Don't worry, weather is getting better now."
'Drinking whisky'
Ms Vardy said: "The Britons that Nigel was with have all come back safe.
"We will get full confirmation when people have talked to him - so, good news.
"We just need now the 'Nigel is drinking whisky in a