The survey showed that 51% of those questioned believed the move would provide West Ham with the resources to improve the squad and build the club.
The other reasons given for supporting the move included growing the club's supporter base and the belief the Olympic Stadium would provide an improved fan experience.
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.
Those supporters have been offered the chance to take part in on-going consultation sessions throughout this summer.
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."
MG 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.
The results have been published on West Ham's official website whufc.com.