Transactions at RBS branches are down almost 30% since 2010 and the bank needs to offer "smarter solutions" for its customers, Ross McEwan said.
In one of his first speeches in the role, Mr McEwan said RBS has to confront "seismic shifts" in banking.
The use of mobile apps and "self-service centres" can increasingly meet the needs of customers, he said in an address to delegates at a business conference at the Scottish Parliament.
A review of the entire RBS business is under way and fundamental changes have to be made, including embracing new technology and modernising customer service, he said.
The bank expects to have three million customers using its mobile banking app by the end of the year, Mr McEwan said.
"At the same time, we are seeing less and less activity in our branches. Since 2010, branch transactions are down almost 30%. The world is changing dramatically and as we consider the radical change we have to make, we need to prepare for a future based on being there for customers on their terms and not on our terms."
The bank should also look at putting 24-hour self-service centres in places such as Waverley railway station in Edinburgh, he said.
"These machines can address the vast majority of the day-to-day banking needs of customers. Then instead of answering balance inquiries at a branch, branches should be the places where people go because they need advice, they need a mortgage, they need actual help with their financial position."
The review is focused on returning to the needs of the customer, he said, adding that he is "not nostalgic" about banking.
"We need to harness the new-found power of the consumer, embrace the technologies that are enabling it and make ourselves simple and easy to do business with. That is not the reality of banking today," Mr McEwan said.
"The review of our business over the next few months will lead to some significant changes. When it comes to that time, you may not agree with all the steps that we decide to take but I hope you have some sense today that our intentions are the absolute right ones and that we are focused on our customers."
No compromise would be made on the "safety and soundness" that he said his predecessor Stephen Hester built since the economic crisis began in 2008.
"RBS was saved by the taxpayer at an enormous expense," he said. "We must never put this country in that position ever again.
"It's pretty clear to me that we have a very special obligation to the people of this country."
He said he is optimistic about the economic outlook.
"Through our customers we are getting a clear view that the economy has turned, and turned for the better," he said. " They are hiring more people, more of them are asking about borrowing to invest in their businesses than at any point in the last five years.
"Our experience is confirmed by the official figures. The UK is growing above its long-run trend and there are more people in work than there have been before."
© 2013 Press Association