Results published on West Ham's official website show the move to the Olympic Stadium has the backing of 85% of the club's supporters, according to a poll conducted by SMG YouGov.
Only 5% of the 11,858 supporters questioned were against West Ham leaving Upton Park under any circumstances while 10% said they would consider backing the move but they required more information.
West Ham plan to move into the Olympic Stadium, with a post-conversion capacity of 54,000, for the start of the 2016/17 season.
The club's vice-chairman Karren Brady said: "I am delighted that the SMG YouGov independent poll shows that such an overwhelming majority of our fans are in favour of our plans to move to the Olympic Stadium.
"I would like to thank each and every supporter that took the time to have their say on what is an historic and monumental decision for the club.
"We must now engage further with the fans who've requested more information but it is fantastic to know that the consensus among our supporters is that they are behind the move.
"Now we know we have their support to advance this incredible project, we can look forward to the busy, but exciting, three years ahead working together to ensure that this world-class arena exceeds their expectations."
SMG YouGov said the poll was six times larger than typical surveys of 2000 people used for robust research analysis, therefore greatly reducing the margin for error.