"I took a very close interest in the question of the lawfulness of any military action in which the United Kingdom might be involved," Straw, who is currently justice minister in the British government, said.
Straw confirmed he received Wood's advice on January 24, 2003, two months before the invasion, which said acting without a second resolution "would amount to a crime of aggression".
He read this "with great care, and gave it the serious attention it deserved", before replying: "I note your advice, but I do not accept it."
Straw explained on Monday that there was a "striking contrast" between this later memo and one Wood wrote in December which set out a balanced view stating both why a second UN resolution was needed, as well as why it was not.
"The advice that he gave was contradictory," Straw said.
In the end, Straw noted, Peter Goldsmith, the former attorney general, decided in February 2003 that a second UN resolution was not needed and this was the "definitive legal advice" which justified war.
The inquiry, which began in November, heard from Tony Blair, the former prime minister, on January 29.
Sir John Chilcot, the probe's chairman, has said Blair could be called to testify again, while Gordon Brown, the prime minister, is due to appear in the next couple of months.