TSB's mobile banking app and online service are "up and running", the bank's boss has said after more than two days of delays that saw customers unable to access their accounts.
Chief executive Paul Pester announced on Twitter on Wednesday morning that the services had been restored and thanked customers, many of whom had been left furious by the outage, for their "patience and bearing with us".
TSB had intended to complete a major IT system upgrade on Sunday evening, although problems persisted into a third day.
Delays meant customers were left unable to access their money online, while some reported being able to access other customers' accounts.
On Tuesday Mr Pester said he was "deeply sorry" for the problems as data and banking watchdogs confirmed they were looking into the situation.
He said on Twitter on Wednesday morning: "Our mobile banking app and online banking are now up and running. Thank you for your patience and for bearing with us."
MPs have demanded answers from the bank about the IT meltdown.
Treasury Select Committee chairwoman Nicky Morgan wrote to Mr Pester asking for details of the problems and the bank's response.
She said: "This is yet another addition to the litany of failures of banking IT systems.
"Potentially millions of customers could be affected by uncertainty and disruption.
"It simply isn't good enough to expose customers to IT failures, including delays in paying bills and an inability to access their own money.
"Warm words and platitudes will not suffice. TSB customers deserve to know what has happened, when normal services will resume, and how they can expect to be compensated."
Customers complained of problems with mobile and online accounts several hours after a system upgrade was supposed to have been completed on Sunday.
One customer said they had "access" to other customers' accounts totalling more than £20,000 and another reportedly discovered they had been credited with £13,000 after logging back in.
A number of customers complained that they were still unable to access their money on Tuesday.
The Information Commissioner's Office, which monitors data and privacy, said it was "aware of a potential data breach in relation to TSB and are making inquiries".
Banking regulator the Financial Conduct Authority said: "We are aware of the issue and are liaising with the firm."
The upgrade window was scheduled between Friday at 4pm and Sunday at 6pm.
The bank had told its account holders that some of its services, including online banking, making payments or transferring money, would not be possible over the weekend.
TSB said a "tiny fraction" of customers saw accounts belonging to other customers and the issue was resolved in about 20 minutes of it emerging on Sunday.