Crosbie replaces Paul Pester, who resigned in September after months of pressure over the botched IT system switch that locked nearly two million customers out of online banking services and led to a surge in accounts hit by fraud.

Crosbie joins from banking group CYBG PLC, where she has worked for more than 20 years, most recently as chief operating officer.

She will become the only female CEO of a major British bank when she joins TSB in 2019.

Executive chairman Richard Meddings will return to his non-executive chairman role when Crosbie joins TSB.

He told reporters Crosbie's appointment was "a big step" in the bank's turnaround. He said the group had fixed most of its IT issues.

"By the end of this year we will have put [these IT problems] behind us," he said. "I do believe we can look to the future to 2019 and beyond with real confidence."

Crosbie, who is in her late 40s, will be paid a higher basic salary than predecessor Pester – who was on 913,500 pounds – and put on a "similar" bonus and incentive plan, Meddings said.

Financial services companies have come under pressure to hire more senior women to tackle the finance industry's dismal record on gender equality. But Meddings said this had not influenced the decision, saying: "We simply chose the best candidate."

Meddings said the first part of a long-awaited report by law firm Slaughter & May into the TSB's IT outage would be published before the end of the year, with the full findings to follow in the first half of 2019.

Pester gave up a 2 million pound bonus linked to successfully completing the IT upgrade and may have to give up further awards depending on the outcome of the investigation.

Despite the high profile IT issues, relatively few TSB customers have jumped ship to rivals, according to Pay.UK data, with a net loss of just 17,000 of its 5 million customers in the second quarter when the outage happened.

Sabadell has estimated that the total bill for the outage will be at least 320 million euros this year.

Meddings said the TSB brand remained strong and added: "It's clearly bruised, but not fractured". Meddings also said the bank's customer account deposits had increased over the year.

(Additional reporting by Dasha Afanasieva; editing by Jane Merriman)

By Iain Withers