The Edinburgh-based bank has been stung by a £43 million charge to refund interest and charges to 200,000 credit card customers who received late or inaccurate statements over the last five years.
It has also made another £20 million provision for compensating those mis-sold payment protection insurance, taking its total PPI bill to £240 million.
The problems in its credit card business, which will lead to an average pay-out of £215, occurred between 2008 and 2013, after Tesco bought out its joint venture partner Royal Bank of Scotland for £1 billion.
Tesco chief executive Philip Clarke said he was not worried that the compensation issues would affect the launch of its current account, which it has said will be a simple and transparent alternative to those currently on offer.
"It is really proper that we make provision for past mistakes, mistakes shared by the whole of the banking industry, or a large and significant part of it," he added.
Mr Clarke said he is "incredibly proud" of the work being done at the bank, which employs 3300 people in Scotland out of a total workforce of 4000.
But he added: "We have to acknowledge that mistakes were made in the past, principally around PPI."
Tesco Bank is due to launch its current account by the end of June.
The £43 million will be used to repay interest and charges racked up by affected customers.
The compensation charge came after the Office of Fair Trading (OFT) wrote to lenders in November seeking confirmation that they were complying with the Consumer Credit Act.
Tesco Bank said that after the OFT's intervention it stepped up an earlier investigation into "historic operational issues".
"As a result the group has determined that it is appropriate to compensate certain customers affected by these breaches," it said.
Tesco warned that the final bill for compensating credit card customers was uncertain because oversight of consumer credit passed to City regulator, the Financial Conduct Authority, at the beginning of April.
Some other banks have also been affected by similar problems including Northern Rock which said at the end of 2012 it would hand over £270 million to 150,000 customers.
In September Barclays said it would pay out £100 million to 300,000 customers due to similar issues. RBS and Lloyds, owner of Bank of Scotland, are looking at their credit card businesses to see if they have to compensate customers.
A spokeswoman for Lloyds Banking Group said: "We are committed to ensuring that we provide our customers with the right information about any credit agreements that they have with us.
"We have taken part in the OFT exercise and are now working to address cases where this has not happened.
"We will contact any affected customers in due course."
Tesco Bank has so far paid PPI mis-selling compensation to 47,300 customers and expects another 10,300 to settle with the institution.
Despite the compensation claims, Tesco Bank's pre-tax profit for the year to February 28 rose 23.1% to £152.6 million.