The existing coaching staff - Kevin Nolan, Paul Nevin, Stuart Pearce and Xavi Valero - have all extended their contracts with the club after manager David Moyes agreed a new three-year deal.
The Hammers have also confirmed that they are "close" to appointing a new head of recruitment at the London Stadium, a long-term ambition of Moyes's since his return to the club.
McKinlay, who had been at Stoke City, worked at West Ham during Moyes's first spell at the club. Nick Davies, who worked at the club during the same spell, has also returned as part of the fitness staff having been at West Brom.
Moyes's long time assistant Irvine stepped back into a consultancy role at the end of last season for personal reasons after helping the Hammers finish sixth and qualify for the Europa League.
“I’m delighted to welcome back both Billy and Nick," said Moyes. "They bring a wealth of experience and expertise to the team, they know the football club well, and they will fit straight back in to how we work.”
On the new deals for his current staff, Moyes added: “It was very important to me that we did this together.
“The progress so far at the Club has been a real team effort and my staff, not just the coaches, have been a crucial part of that. We are looking to continue to build on what we have done so far and we will work to keep our levels high.”