Mr Brown, who was originally from Cambridge and ran a guiding business from Fort William, died in what Police Scotland said was a fall on the UK's highest mountain.
In a post on his Facebook page, the family of Mr Brown said the 33-year-old experienced climber had been enjoying some free time on a beautiful day in the mountains.
Police Scotland said it had been alerted around 11.15am on the morning in question that a man had fallen at Zero Gully on Ben Nevis. Following a mountain rescue, the body of Mr Brown was recovered.
There are no suspicious circumstances surrounding the death and a report has been submitted to the procurator fiscal.
Mr Brown's family added: 'Anyone that knows Rob knows he is experienced, calm, confident and not a risk-taker on the hill and Friday was no different.
'It was a tragic accident that couldn’t have been prevented and we want everyone to know it was quick and painless for him. He left us whilst having a great day out and was happy and content with his life.
'We are all absolutely heartbroken and devastated that he has had to leave us when he had so much more life left to give and with such an exciting future ahead.
'We are grateful for everyone who has reached out to us so far - to help and support us in so many ways - whilst we navigate the unimaginable.
'Thank you to the Lochaber Mountain Rescue Team members who helped retrieve Rob and his belongings. Many of whom knew Rob personally and we are so grateful.
'We would like to host a celebration of Rob’s life in the next few weeks and will share plans and a date when we can.
'It would mean the world to all of us if you knew Rob and could join, to help share your memories and stories of him.'
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