TfL spent £85m paying off Bombardier, the firm originally appointed for the work, whose contract was a "disaster for London", an assembly report said.
It means District, Circle, Metropolitan and Hammersmith & City lines upgrades are not due to be complete until 2023.
TfL said work was now "well under way" and it had taken action to cut costs.
More on this story and other news from London
Following publication of the report by the assembly's Budget and Performance Committee, its chair John Biggs said the Sub-Surface Upgrade Programme (SSUP) work was not going to be of benefit to passengers "any time soon".
"This is because TfL has grossly mismanaged its signalling contract with Bombardier," he said.
"[It] leaves TfL with £886m less to spend on its capital programme than it thought it had."
TfL's auditors KPMG said in a 2014 report the procurement process was flawed, with Bombardier's bid taken forward despite the company failing to show it could do the work.
When it became clear that the firm was failing to deliver, the wording of the contract meant it had to pay the company for the money it had spent rather than the value of its work.
Mayor of London Boris Johnson, said Bombardier - awarded the contract in 2011 - had "totally stuffed it up".
A contract was subsequently awarded to Thales, but the committee said TfL continued to claim the project could be delivered by 2018.
"No-one in TfL has been held to account, and the mayor, who chairs its board, serenely and indifferently acts as if a £900m increase to the budget isn't an issue," said Mr Biggs.
"In government, heads - political or official - would roll after such financial mismanagement.  At TfL the key players have been promoted and nobody was to blame. It is a scandal."
A TfL spokesman said work on the SSUP upgrade was "well under way" and it was implementing a £16bn savings programme.
"It was essential that decisive action was taken to end the old Bombardier contract as soon as it became clear that it would not deliver for London," he said.
"As the assembly acknowledges, we have implemented the central recommendations from KPMG's independent review."
The BBC has approached Bombardier for comment.
Four Tube line upgrades will be five years late and £886m over budget after "gross mismanagement" by Transport for London, the London Assembly says.