The applications for the expansion, considered by the London Borough of Newham, were for full consent for the demolition of existing buildings and structures at the airport to provide additional infrastructure and passenger facilities and outline consent for a new 260-bed hotel.
The approval will also enable the airport to operate up to a permitted 111,000 annual flights, from the 70,000 currently flying.
According to a planning report, a total of 1,362 responses were received from local residents, comprising 21 in support and 1,330 objecting to the application.
The report said a key objection to the plans was additional noise. But it said the development would result in "not significant increases in noise exposure".
However, it added, it recognised "that there will be an increase in the number of people exposed to noise, as the population around the Airport will continue to grow".
The compensate for this, the report recommended an "improved sound insulation scheme must be secured through the S106".
The approval was subject to 131 separate planning conditions to reduce the potential impact of the development. These include:
• A limit of six million passengers passing through the airport a year, with quarterly reports submitted to the council
• The noisiest night time construction piling work can only take place during 32 weekends
• A noise barrier to be constructed on the south side of the site during the construction period.
Local community benefits will include funding to bolster transport services including a bus turnaround at the new Custom House Crossrail station.
The plans could yet be called in by London mayor Boris Johnson or communities secretary Eric Pickles.