Irvine and Woods served alongside Moyes during his first spell at West Ham, while McKinlay is now the assistant manager of Stoke City.
Moyes admits his first task will be moving the club away from danger, the Hammers now just one point and one place above the Premier League's drop zone following their defeat to Leicester on Saturday.
"There is money there to spend if we need to but I'm more interested in the players we have got and moulding them into the best possible team and get results", he said. He recorded nine wins and 10 draws from 31 games in his first spell, leading the club to Premier League safety.
West Ham sits a point ahead of the drop zone, with a match-in-hand on its relegation rivals.
He replaces Manuel Pellegrini, who was sacked after Saturday's 1-2 home defeat by a much-changed Leicester side.
The exciting future is yet to materialise and asked to explain why he might be the right man now, having been the wrong man 18 months ago, Moyes said: "I have always felt I am an extremely experienced manager".
"I'm really that thrilled to go again and I'm going to make it impossible that the clause can't be implemented", Moyes said of an 18-month contract that contains an extension clause.
"He's been there before, he knows the club, and I think he will lift the place, get a bit of confidence in the team and bring smiles back onto the faces of the players and the fans". There is a clause in my contract to extend the deal.
"I think the squad of players I have here is a better squad of players than when I took over before, so I'm eager to work with them".
Irvine is set to re-join Moyes' coaching staff after assisting the ex-Manchester United boss in his previous roles with Everton and Preston North End.
"David proved in his short time with the club that he was capable of getting results", Sullivan said.
"I'm a very experienced Premier League manager with arguably only one or two more experienced than me", Moyes added.
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