Sports journalist Pete O’Rourke who broke the news says the player will now undergo a medical before the transfer is completed.
A report yesterday suggested West Ham rejected £3.5m bids from both Middlesbrough and Sunderland for Randolph services.
West Ham will not stand in Randolph’s way after the arrival England international Joe Hart on a season long loan.
The 30-year-old made 22 appearances last season when he got his chance after a drop in form by Adrian, he has later replaced himself when he experienced a bad run of games and Adrian retook the Goal keepers jersey for the remainder of the season.