Payet made his Premier League debut for the Hammers on Sunday afternoon, playing for the entire 90 minutes against Arsenal at the Emirates Stadium.
The France international was hugely impressive against the Gunners, helping West Ham to a 2-0 victory.
Former West Ham defender Ferdinand was following the game, and he was impressed with the performance produced by Payet on his Premier League debut.
Payet showing great promise too....quick with vision!— Rio Ferdinand (@rioferdy5) August 9, 2015
Payet, who joined West Ham from Ligue 1 outfit Marseille in June, was one of the best players on the pitch at the Emirates.
During the first half, the 28-year-old had a pass accuracy of 93%, put in three crosses, attempted two dribbles, took one shot and provided one assist.
The Frenchman has been arguably the most exciting signing of the summer so far for West Ham, and there is more to come from him yet.