The Royal Navy ship is carrying supplies including 12,500 blankets, 20,000 candles, 30,000 bags of rice and 9,800 tins of sardines.
Thousands of tins of vegetables, shelter kits, jerry cans and water carriers are also on board.
The supplies have been provided by the Government's Department for International Development (DFID).
Typhoon Haiyan - said to be the strongest ever to make landfall with winds of up to 170mph - hit the Philippines on November 7, killing thousands and leaving many more without food and shelter.
HMS Illustrious is replacing HMS Daring, which has been distributing aid in remote communities for the past week.
Seven helicopters are on board to help get the aid quickly into remote areas.
The ship was off the east coast of Africa on counter-piracy operations when it was diverted to help the relief effort.
It is expected to stay in the Philippines until early December.
Defence Secretary Philip Hammond said: "The crew of HMS Daring have done a fantastic job in the Philippines and I am pleased that HMS Illustrious will be able to continue this good work by providing substantially increased helicopter capability, ensuring relief reaches all those stricken by Typhoon Haiyan."
The UK public has now donated more than £60m through the Disasters Emergency Committee Appeal and the Government has given more than £55m.
The death toll from the disaster has risen above 5,000, according to the Philippine government, with around four million people displaced and more than 1,600 still missing.