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Woodward has overseen deals that have brought in Matteo Darmian, Memphis Depay, Morgan Schneiderlin and Bastian Schweinsteiger this summer.
But United missed out on transfer target Pedro, with Barcelona's Spain winger, 28, opting to join Premier League rivals Chelsea.
"Every day I am updated by him and I trust him," said Van Gaal.
"I have the idea you want to separate Ed Woodward with me. Never. Never."
Van Gaal was speaking at a news conference ahead of United's home game with Newcastle on Saturday.
He added: "I don't think [the critics] have to doubt Ed Woodward because he has proven already for many, many years he is the right person on the right spot."
And the 64-year-old is confident when United want a player, Woodward will bring him to Old Trafford.
"When Manchester United want a player, he shall come," he said.
"You can see my selection and you can see for every position we have a double. We don't have to [buy] but if we can do it to improve we will."
However Van Gaal said he did not want to "interfere" regarding the club's interest in Southampton's 23-year-old midfielder Sadio Mane.
He added: "I cannot answer that question either because I cannot interfere. I don't want to interfere. It's for Ed Woodward doing the things and he does it very well, I think."
The Dutchman did suggest Schweinsteiger, 31, may be in line for his first Premier League start.
The Germany international replaced Michael Carrick at half-time during United's 3-1 win against Club Brugge on Tuesday.
"Maybe it shall happen tomorrow," Van Gaal told MUTV.
"We have seen a solution in rotating our [second] captain, Michael Carrick, with Schweinsteiger.
"I think it's a very good solution because we can spare them both for the big moments."
One man who will not feature is goalkeeper David De Gea, 24, who is linked with a move to Real Madrid.
"We shall evaluate [whether he can play] after 1 September," said Van Gaal.
Manchester United boss Louis van Gaal says he trusts executive vice-chairman Ed Woodward with club transfers.