The business, owned by state-backed Royal Bank of Scotland (RBS), has made the provision as part of a review of advice to clients dating back to 1950.
It comes days after RBS was fined £14.5m for serious failings in its advice to mortgage customers from June 2011 to March 2013.
The group, which is 80 per cent-owned by the taxpayer, has also put aside more than £4 billion for mis-selling payment protection insurance and interest rate swaps - complex financial products it sold to small firms.
Coutts chief executive Michael Morley has already written to 15,000 customers warning them there had been "some instances where the advice given during our previous advice process could have been better".
It is understood the £110m will come from a £206m provision RBS has made for the private bank. But it is the first time the cost of this particular issue, detailed in the Coutts accounts, has been made public.
This comes after the business agreed to review investment advice following new rules from the Financial Conduct Authority in November 2012.
The provision is not the first time Coutts will have had to pay out for mistakes. In March 2012 it was fined £8.75m for failing to ensure it was doing enough to be certain it was not handling laundered money, and a £6.3m penalty for misleading customers over a savings product linked to bailed-out US insurer AIG.
RBS said at the time of its half-year results this year Coutts had decided to undertake a past business review "into the suitability of investment advice provided to its clients", following a 2013 review by the FCA.
It said: "This review is ongoing. Coutts & Co is in the process of contacting clients and redress will be offered in appropriate cases. A provision has been taken to cover any potential liability arising from this review."