The France international winger moved to the Hammers from Ligue 1 outfit Marseille last month, as announced on the Premier League club’s official website.
Payet has signed a five-year contract with a further one-year option for an undisclosed eight-figure fee.
The 28-year-old is still on holiday, but Dicks has stated on Twitter that he will start training tomorrow.
Great signing for West Ham United
Payet was one of the best players in Ligue 1 last season, helping Marseille finish fourth in the league table.
The former Lille star scored seven goals and created 134 chances in 36 league appearances.
The 28-year-old had a pass accuracy of 80% and a shot accuracy of 47%, and won three headers, 66 dribbles and 17 tackles.