Rob Whiteman told the Home Affairs Select Committee cases received but not entered into the UKBA's system should be cleared by March.
Last month, Chief Inspector of Borders and Immigration John Vine revealed that thousands of immigrants were allowed to stay in the UK without undergoing proper checks due to a huge backlog of applications.
UKBA staff dealt with cases so inefficiently that at one point 100,000 pieces of post were unopened, Mr Vine said.
He had been asked to assess how well UKBA had handled the backlog of thousands of unsolved cases.
Committee chairman Keith Vaz MP asked Mr Whiteman if he could confirm the size of cases for entry to the UK that have been received but not put on the agency's database.
After hearing the figure was 50,000, Mr Vaz said: "You have given me a straight and astonishing number."
Mr Whiteman said the backlog would be dealt with by March.
He said: "You must remember we receive one million applications a year. We work on the basis that we want all cases put on the system in a week."
Immigration minister Mark Harper said 50,000 cases was the equivalent of two weeks' worth of applications.