The summer recruit also says he is looking forward to working with current number one 'keeper Adrian.
The former Croatia boss was appointed as Sam Allardyce’s replacement at Upton Park last month after months of speculation and numerous other candidates being linked with the role.
He joins the Hammers after managing Besiktas in Turkey, where he also guided them in the Europa League, a competition his new side will be competing in this season as well.
It is thought he has been appointed to bring a more attacking style to the club, and Randolph says everyone should be happy with his arrival.
“He likes attacking football and everyone should be happy,” he told the official website.
“I am happy to get back started and see how the new manager does things. It is very good to be here with some new faces and new team-mates. The move came about at the end of last season and I jumped at the chance to be in the Premier League.”
The Republic of Ireland international joined the club on a free transfer from Birmingham City last month, becoming their first signing of what is likely to be a busy summer of arrivals and departures.
Current number one Adrian was impressive for the Hammers last season though, and it will take some work to replace him. Randolph however, insists he is looking forward to working with his competition for the 'keeper’s jersey.
“I saw the game when Adrian scored against Everton last season and he had some fantastic games last season. I am looking forward to working with him,” he added.