In an interview with the Washington Post newspaper, Mr Bush described the deal as the "right package for the moment".
Beijing has lodged a formal diplomatic protest, saying the sale could jeopardise relations.
Taiwanese President Chen Shui-bian welcomed the arms sales and thanked the US Government, Congress and what he described as Taiwan's American friends.
A statement released by Mr Chen's office in Taipei said the arms sales would help ensure Taiwan's security and "maintain stability across the Taiwan Strait".
The US president said he was not worried that Chinese objections to the sale would cause relations between the two countries to deteriorate further.
"The Chinese must understand that we have got common interests.
"But there is going to be some areas where we disagree and, evidently, one area where we disagree is whether or not the United States ought to provide defensive arms for Taiwan, which I have done," he said.
Duty to Taiwan
In a separate interview, Mr Bush told ABC Television that the US had a duty to aid Taiwan in case of attack by China and would do "whatever it took" to help the island defend itself.
And President Chen echoed this saying Taiwan had to buy the weapons because China would not renounce the use of force against the island.
He called on Beijing to reduce the number of missiles deployed along its east coast which are targeted at Taiwan, and to enter into a dialogue with the island to normalise relations between the two sides.
The White House has given Taiwan a full list of the weaponry it will receive.
Taiwan arms sale
4 Kidd class destroyers
12 P-3C Orion anti-submarine aircraft
8 diesel submarines
The list includes submarines, warships and anti-submarine aircraft, but not the sophisticated naval combat radar system Aegis, which the Taiwanese had requested.
Mr Bush said he did not expect the sale, or the recent stand-off over China's holding of the US spy plane and crew, to affect his state visit to China in the autumn.
"I am going to go over to Shanghai in the fall and fully expect that the invitation that has been extended to me will continue to remain in place," he said.