Alexei Likhtman, 44, lost balance while taking photographs and fell around 50ft on a trip to part of the Appalachian Trail in Maryland, local police said.
Other hikers tried to save him but he died about an hour later, at noon local time on Sunday.
A spokesman for Maryland Natural Resources Police said Prof Likhtman was in the US to attend a conference in Baltimore and had been visiting a section of the long-distance hiking trail called Annapolis Rock with a PhD student, named as Jian Zhu, also from Reading.
Lieutenant Art Windemuth said: “About 10.45am the victim was photographing the area and tripped and fell approximately between 40 and 50ft.
“People in the area immediately began first aid and called 911. Emergency personnel arrived and immediately began first aid, but the victim was pronounced deceased about noon.”
Lt Windemuth said Prof Likhtman had been leaping on rocks when he tripped, while the student was uninjured.
He said: “He was with a student of his and was taking photographs. He had a tripod with a camera on it, the camera fell and he fell. He was jumping from rock to rock when he tripped.”
Prof Likhtman’s body was transferred to the office of the chief medical officer in Baltimore for a post-mortem examination to be carried out.
His family has been informed of his death.
According to his Facebook and LinkedIn social media accounts, Profe Likhtman was originally from Moscow before moving to the UK to study and teach.
He worked as a lecturer at the University of Leeds between 1999 and 2007 before taking up a post of professor of mathematical physics at the University of Reading, working in applied mathematics. He was also the departmental director of postgraduate research studies.
The Appalachian Trail is a 2,200-mile hiking trail in eastern America, stretching from Maine in the north to Georgia in the south.
It was brought to wide appeal by the Bill Bryson book A Walk In The Woods, made into a recently-released film of the same name starring Robert Redford and Nick Nolte.
A statement from Reading University said: “It is with regret that we can confirm the tragic death of Professor Alexei Likhtman, professor of Mathematical Physics at the University of Reading. Our thoughts are with his family and friends during this difficult time.
“Professor Likhtman was a highly valued, well-loved member of staff who had been due to attend a conference in Baltimore before the accident occurred.
“The University was informed of his unfortunate death last night and is liaising with the authorities in the US. We are providing support to staff and students and will be saying more as soon as we can”.