In January 2003, Wood wrote to Straw: "I hope there is no doubt in anyone's mind that, without a further decision of the council ... the UK cannot lawfully use force against Iraq to ensure compliance with its Security Council WMD resolution."
Wood said the minister brushed his concerns aside, taking the view that "international law was pretty vague".
'No legal basis'
The evidence came just days before Tony Blair, the former British prime minister who sent UK troops to Iraq, appears before the inquiry.
Some critics of the conflict have argued that he should face prosecution for a breach of international law, although experts say this is unlikely.
Blair justified the invasion over Saddam Hussein's continued defiance of UN Security Council resolutions governing his possession of weapons of mass destruction.
Peter Goldsmith, the then attorney general and prime minister's chief legal adviser, gave the green light for the action on the eve of the March 2003 invasion, saying that UN resolution 1441, passed in November 2002, provided a base for military involvement.
But Wood told the inquiry that he had consistently advised that regime change was not a legal basis for war, and action required a specific UN mandate, which was absent in resolution 1441.
"I made it clear that, in my view, the draft that they were working towards did not authorise the use of force without a further decision of the Security Council," he said.
The lawyer's testimony is the first time he has expressed his opinion on the war.
Al Jazeera's Nadim Baba, reporting from London, said: "What we've heard today has really enforced that the advice that the lawyers were giving to the British government in 2002 and 2003 was consistent.
"They have stressed that hey were all singing from the same hymn sheet and that they were telling the politicians that it was not lawful to take military action without a United Nations Security Council resolution on top of resolution 1441."
Wood's deputy at the time, Elizabeth Wilmshurst, who also gave evidence to the hearing on Tuesday, resigned just before the invasion because of her opposition to the conflict.
She said that she believed Goldsmith agreed with the foreign office lawyers until he delivered his legal opinion.
"The formal advice wasn't asked until the very last moment, when really it would have been very, very difficult for him to give a different view without giving a major public relations advantage to Iraq," she said.
Goldsmith is due to appear before the inquiry on Wednesday.