Dr Murray, a physical activity champion for the Scottish government, will begin by climbing Ben Lawers – Britain’s tenth highest mountain at 4am on 19 July.
With running partner Donnie Campbell, a running coach and former Marine commando, Dr Murray will then target nine further peaks – all in Scotland and 1,200m high or more.
Dr Murray says the challenge – dubbed ‘The Big 10’ – has never been done before to his knowledge.
He hopes to inspire people to exercise more ahead of this summer’s Commonwealth Games in Glasgow, and in support of the Scottish Association for Mental Health. Dr Murray said: ‘This will be a tough but beautiful shift, but what we are hoping to do is raise awareness of the benefits of exercise, and being in the great outdoors.
Raising awareness of exercise
‘We know for example that even doing 30 minutes walking five days a week has been shown to make people happier on average, and live 7.2 years longer.’
Mr Campbell said: ‘It is a totally do-able challenge, and we hope people will give "The Big 10" a shot after us’.
Dr Murray is also encouraging companies to take part in schemes like ‘Fit in 14’, which push staff to take small steps towards a more active lifestyle.
In 2010, Dr Murray ran 2,559 miles from John O’Groats to Morocco as well as taking part in the North Pole marathon.