Illustrious will replace HMS Daring, which has already been deployed to the archipelago. The carrier’s helicopters could be used to airlift food and water to survivors stranded in remote parts of the island nation.
The ship also has the technology to convert sea water to drinking water.
The Ministry of Defence said that Illustrious should arrive in the Philippines on November 24 or 25, with 900 crew and seven helicopters on board.
Britain’s last remaining aircraft carrier is due to retire from active service next year.
The funds, from online, text and phone donations will be used to deliver food, water, temporary shelters and other supplies to the 11 million people affected by the typhoon.
Mr Cameron said: “What happened in the Philippines is an absolute tragedy. You can see the devastation, the suffering, and it’s quite clear that we are going to need long-term help for those people.
You can see the devastation, the suffering, and it’s quite clear that we are going to need long-term help. David Cameron
“As ever, the British people have been very generous with their donations. The British Government has already pledged over £20 million, which makes us one of the most generous donors anywhere in the world.
“But it’s practical action that’s needed as well. That’s why I sent HMS Daring to go and help in the Philippines and I can announce today that once Daring has started its work, we are actually going to be able to replace in time HMS Daring with HMS Illustrious, which is, of course, a carrier with helicopters – seven times as many helicopters as on HMS Daring and with the key ability to process fresh water, so we will be giving further assistance in the best way we can.”