He said no decisions under the control of the Scottish Parliament will be removed when powers are returned from Brussels.
Mr Mundell’s comments were part of his Fullerton lecture at the International Institute for Strategic Studies in Singapore on Thursday during a visit to south-east Asia.
He said: “It is a real source of pride to me that today, after successive pieces of legislation, the Scottish Parliament is one of the most powerful devolved parliaments anywhere in the world.
“Key decisions are taken in Scotland to address Scottish priorities and needs while Scotland benefits from the pooling of risk and resources that comes from being part of the United Kingdom.
“The devolution settlement is a real success story for Scotland - and Brexit will only strengthen this.
“As we leave the EU, all the powers and frameworks currently held and run by the EU will be transferred back to the UK.
“For me, one of the most important set of choices will be to ensure that these returning powers are held at the right level of government and that the right common frameworks are in place.
“I am very clear that no decisions currently made by the Scottish Government will be removed.
“It is the expectation of the UK Government that the outcome of this process will be a significant increase in the decision-making power of the devolved Scottish Government.”
He said the Brexit negotiations would build “a stronger, fairer, more united and more outward-looking country”.
Mr Mundell also focused on Scotland’s trading relationship with Singapore, which the Scotland Office said ranked fifth globally in terms of food and drink exports from Scotland, worth £202 million, in 2015.
He said: “Scotland, and the rest of the UK, has always looked to the rest of the world and the opportunities it holds.
“A positive, outward-facing approach is what guides the UK as we work with our friends and partners around the world today, as we strengthen those relationships, reinvigorate our partnerships and forge stronger friendships.
“Few friendships have deeper cultural and historic roots than those shared by Scotland and Singapore.
“Singapore is Scotland’s largest trading partner in south-east Asia. And it’s not hard to see why. Those people-to-people links mean we understand each other and can build trust.”
The lecture is part of a trip to Singapore and Burma promoting Scotland’s business interests, including whisky, technology, oil and gas.