Repair costs for the Elizabeth Tower in the Palace of Westminster have now doubled to an estimated £61m, parliamentary authorities have said.
The project is more complex and extensive than originally thought, when the estimate of £29m to £45m was made.
While there were "unique challenges" in working on a historic site, Parliament said it was disappointed at the rising bill and would launch a review.
Big Ben chimed for the last time in August pending the work beginning.
The rising cost was announced as Parliament confirmed it had appointed construction firm Robert McAlpine to carry out the renovation, which could take up to four years, following a tendering process.
The authorities said the revised figure followed more detailed and technical assessment of the 160-year-old Tower's condition, including the state of stonework and the cost of removing and repainting the metal in the tower and reglazing the clock face.
More extensive ground works will be required in the Palace of Westminster, due to the quantity of pipes and other utility-related infrastructure under the surface, to support the scaffolding required.
While the estimated cost of the work has risen from £29m to £44m, the level of contingency funding to be put aside in case of "unexpected events" has gone up from £5.8m to £17.2m.
The authorities also said they had transferred the cost of fire safety work, due to be carried out as part of another project and already budgeted for, to the restoration of the tower.
They said they had "expressed their disappointment in the cost increases, and the unreliability of the original estimate" and "instructed officials to provide regular updates on progress".
"In advance of tendering contracts, the initial high level estimates were set at a lower level to avoid cost escalation from the market," they said in a statement.
"Subsequent estimates, using better data and more extensive surveys, better reflect the true likelihood of the costs. We believe that we now have a more accurate estimate of the cost of the works and will report regularly to the committees on the progress of work."
The news that Big Ben would not sound again before 2021, except for special occasions such as New Year and Remembrance Sunday, prompted criticism from Theresa May and other MPs.
The House of Commons said it would look again at the duration of the project and the scope for hearing the bell's famous bongs more often.