Jayanta Brahma, 38, completed the epic feat at The Climbing Lab in Kirkstall.
Olympus Mons, the tallest mountain in the solar system, is located on Mars and is 22,000 metres high.
It took the biomedical scientist, from Knottingley, 37 weeks to complete the challenge in 5,500 individual ascents of the centre's indoor climbing walls. He worked at a rate of 80-90 climbs per hour during his sessions.
Jayanta, a father who works at Leeds General Infirmary, decided to undertake the climb to raise money for the Brain Tumour Charity.
"I decided to do the challenge as a metaphor for the struggles of life - we can make molehills out of mountains sometimes. I started out with a decision to raise money for the Brain Tumour Charity, as this area of health has been a recurrent theme in the lives of several around me over the past few years; in order to fund their quality of life improvements and life-saving research.
"As I got more into the challenge, I quickly learned that rock climbing is extremely good for improving mental health. Having been struggling with psychosis, depression and anxiety myself, I found that not only the exercise itself, but also the community and talking about my issues broadly (along with clinical care of course) brought everything under a very controllable level and set me on a noticeable road to recovery.
"Mental health is a very important topic, due to the stigma and taboo associated with it, and I feel I am helping that to change. It affects everyone in some way, including those under the care of the Brain Tumour Charity. I completed the climb last Friday, having been climbing for eight months."
He will also feature in a short documentary film about his journey.