The City regulator imposed the penalties after an investigation into the scandal, first revealed by The Herald in 2010, found the bank and its sister operation Yorkshire Bank had unfairly forced 22,000 customers into higher mortgage repayments in order to rectify an error by its staff.
The overall cost to the Clydesdale of the judgment is expected to be around £42m, including compensation on top of the £8.9m fine.
The mistake was caused by a glitch in the software which calculated repayments and resulted a £21.2m shortfall for the bank. For customers, the shortfalls ranged from less than £20 to more than £18,000, with an average of £970.
The bank tried to pass all of the costs on to its customers and wrote to thousands affected informing them that their repayments would go up, sometimes by as much as £200 a month.
However, many were not informed they could have rejected demands to repay the missing amounts, and the bank is now to pay the price for infringing their rights.
People from across the UK contacted The Herald three years ago after receiving letters telling them their monthly mortgage payments were going up.
Aberdeen psychologist Norrie Silvestro saw his payments rise by 22%.
He said yesterday: "I received compensation but it only came about because of the publicity and the subsequent investigation by the financial authorities. My view is that this was sheer incompetence and someone should have taken responsibility.
"Instead there was the stress and frustration of receiving the letter and having to deal with the call centre when this should have been handled on a one-to-one basis with my bank manager."
He added: "If this acts as a focus for the bank to be more responsible in they way they treat their customers then it's appropriate."
Tracey McDermott, the FCA's director of enforcement and financial crime, said: "Clydesdale failed in its basic duty and, when it discovered the problem, sought to pass all of the consequences on to its customers - expecting them to remedy mistakes which were entirely of Clydesdale's making.
"Clydesdale is paying the price for its decision to put its bottom line ahead of the need to ensure its customers were treated fairly."
Customers who were left with shortfalls will automatically be compensated and the bank is writing to all customers affected by the blunder. Mortgage holders need not do anything until they are contacted by Clydesdale.
David Thorburn, chief executive of Clydesdale, said he was sorry the situation had not been handled properly.
He said: "We should have made it clear at the time that this was entirely our fault and some customers may be entitled to compensation.
"Our priority is to fix this for customers as quickly as possible and they will each receive a letter explaining how we will make this right for them."
Some 14,000 customers will see an "immediate resolution", including a full apology and a refund within the next 48 hours, he said. The majority of other customers with more complicated cases should hear from the bank in the next couple of weeks.
Some customers may also be entitled to compensation for extra charges they have had to incur as a result of the original mistake, such as bank charges.
Consumers can still take their case to the financial ombudsman, which resolves disputes between consumers and financial institutions, if unhappy.
The bank's "lack of clarity" was made worse by poor instructions given to call handlers for dealing with phone calls of complaint, the FCA said. The regulator said the fine would have been higher had it not been for the bank's redress scheme, and it received a 30% discount for settling at an early stage.