Hammers skipper Mark Noble presented the shirts to William and his wife Kate -- with the names of their children, four-year-old George, and two-year-old Charlotte, on the back -- when they paid a visit to the club's home ground, the London Stadium, on Wednesday.
"Right colours, wrong team," jested William, who was also accompanied by his brother Prince Harry as they were there for the graduation ceremony of dozens of sports coaching apprentices.
Noble said whether the children would ever get to wear the shirts was open to debate.
"It was just a little gift from West Ham really," said Noble.
"We know William is an Aston Villa fan - whether they (the shirts) will get put on or not, I don't know.
"It's just a gesture from us to welcome them to the club."