Palace have won the race to sign Gayle breaking their transfer record to land the 22-year-old striker.
A host of Premier League and Championship clubs are thought to have enquired about Gayle, who scored 13 goals in 29 games for Peterborough last season.
MacAnthony believes Palace have got a bargain in Gayle and has backed him to be a big success in the Premier League.
"Just want to wish Dwight Gayle all the best in scaring the life out of Prem League defenders for Crystal Palace," MacAnthony wrote on Twitter. " What a signing for them!
To the people doubting this Gayle move & moaning about value,This boy will score a lot of goals in the prem & make many prem managers look-Daft for not landing him as opposed to signing another foreigner!
"There were 12 clubs who came in for Gayley over June. One of best signings of summer that Palace have made.