The Duke of York began at the 87th floor - just below the top of the 1,016ft tower - and finished half an hour later on level 20.
He was one of around 40 people who completed the task to raise money for educational charity the Outward Bound Trust and the Royal Marines Charitable Trust Fund.
Andrew said afterwards: "I'm not even going to say that was a piece of cake or not. I will never do it again. I have to say, the most difficult bit was walking up the stairs.
"You have a moment to realise what you are doing and where you are going to go. The difficult bit was actually stepping out over the edge so the training I had done over the summer with the Royal Marines in Arbroath gave me the confidence to step out over the edge without too much trepidation.
"When I spoke to [the Queen] last at Balmoral she was interested in why we were doing it and when I spoke to her about all the safety and the activities that were going on around it, about the teamwork, she understood what all the risks were and, like the incredible monarch she is, she was entirely happy.
"But this is not about me, this is about young people, this is about young people's future, this is about changing people's lives and giving them the opportunity."
The royal, who is the Outward Bound Trust's chairman of trustees, raised over £290,000 in sponsorship.
Foreign Secretary William Hague's wife Ffion, who is Outward Bound's deputy chairman, and adventurer Sir Chris Bonington also abseiled down the Shard.