The goalkeeper signed a new four-year deal at West Ham last week.
Randolph joined the Hammers last summer as Slaven Bilic sought out proper competition for current number one Adrian.
He ended up spending the majority of the season doing just that, with most of his appearances coming in the FA Cup.
He impressed when given the chance though, with the club opting to hand him a new four-year contract last week.
And he says that the chance to play at the Olympic Stadium, was one of the factors that convinced him into signing.
“Part of the reason I wanted to stay is because we have a good group of lads and are moving into a new stadium and a new training ground, it’s exciting,” he told the club’s official website.
Randolph will now be hoping that the extra games of Europa League football can see him get more game time under his belt next season.
Should they make it past Astra Giurgiu in the qualifying round, it will see a plethora of fixtures added to their schedule for this season.
That would likely see Slaven Bilic rotate his squad somewhat and Randolph will be hoping he is one to benefit from it should that be the case.