The GLA is due to leave City Hall by 26 November, but delays to refurbishment at its new home at the Crystal building in Newham mean that it will need to use a temporary venue for at least two weeks before the move can be made.
A spokesperson for London Mayor Sadiq Khan said that despite the setback, the move would save the taxpayer £61 million over five years.
City Hall has been the seat of the Greater London Authority since opening in 2002.
The building has been leased by the GLA from the Kuwaiti-owned St Martin's Property Group at a cost of £11 million a year on a 25-year contract.
Some Assembly meetings will still be held at City Hall in early December.
The venue that will host the GLA before it can move to the Crystal building in the East End has not yet been confirmed, though the Barbican Centre has been mentioned as a possible venue.
Sources close to the GLA told the Local Democracy Reporting Service that a number of required changes to the Crystal building including security and equipping the building for Assembly sessions have not yet been completed.
Sadiq Khan's office said that the money saved from the move would be invested in essential services and housing.
A spokesperson for the Mayor of London said: "The Greater London Authority (GLA) is on track to move to the Crystal building in the Royal Docks by Christmas, saving taxpayers £61m over five years.
"As part of the relocation, the GLA will leave its current home near London Bridge on 26 November .
"Assembly meetings scheduled for the first week of December will still take place at the current City Hall and arrangements will be put in place to hold Assembly meetings due for later in the month at a suitable alternative location."
Opposition Assembly members and Newham Council were contacted for comment.