Moyes took charge of West Ham after the sacking of Slaven Bilic this month and the Scot has moved to strengthen his backroom staff ahead of the Premier League trip to ninth-placed Watford on Sunday.
"I know David well from our time together... and it was certainly a big attraction to work with him again, as was the thought of coming to a club like West Ham," Irvine told the club's website.
"This is the sixth job I have been offered since leaving Norwich at the end of last season but it's the first one that has persuaded me to accept," added the 59-year-old, who has managed Preston, Sheffield Wednesday and West Bromwich Albion.
Former Manchester City and Nottingham Forest manager Pearce said he looked forward to helping 18th-placed West Ham improve their form.
"It's tough times at the moment but it's a fantastic opportunity for me. I'm really excited by the challenge," the former England international said.
Moyes said striker Javier Hernandez, who is currently out with a suspected hamstring injury, need not fear being excluded as he was at Manchester United under him.
Hernandez started only six league games in Moyes' spell as Manchester United manager in the 2013-14 season but Moyes said the Mexican would get his opportunities at West Ham.
"He's a top goalscorer, a brilliant finisher," Moyes said. "It was difficult for him at United because I had Robin van Persie, Wayne Rooney, Danny Welbeck, Shinji Kagawa, so there was lots of competition.
"But he'll be treated the same here – if he's playing well and scoring, no problems. If he's not, it will be the same as the rest."
(Reporting by Shrivathsa Sridhar in Bengaluru; editing by Sudipto Ganguly)
