It will be Rooney's fifth major tournament, but in two previous World Cups he has not lived up to the stunning impression he made as an 18-year-old at the 2004 European Championship finals in Portugal.
He was named in UEFA's team of the tournament there after scoring four goals in four games.
At the 2006 World Cup, having barely recovered from a foot injury, he did not score and was sent off as England lost to Portugal in the quarter-finals.
Four years later, when England lost to Germany in the round of 16, his form was again disappointing, while at Euro 2012, having been banned for the first two games, he scored against Ukraine but struggled in the quarter-final loss to Italy.
Hodgson believes that this time he will benefit from a recent break through injury, telling reporters: "I think with Wayne it's a great opportunity this year to really show on a world stage what a magnificent player he is.
"Maybe once or twice in the past I can say without too many fears of contradiction that on the world stage he hasn't exploded as he has on our national stage, where we all accept him as being an outstanding player.
"The message to him is 'This is your chance'. I just rejoice in the fact that he's playing so well."
Rooney has scored 11 goals for United this season, although none since December 26, and has stood out for the champions during an otherwise poor Premier League campaign.
Hodgson said the possibility of Rooney's United team-mate Adnan Januzaj qualifying to play for England was a long way off and added that it is up to the FA's Board to pursue the matter if they want the current rules changed.
Januzaj, who is being wooed by a number of national teams, would not be eligible for England until 2018 at the earliest.
Even then it would require the FAs of England, Scotland, Northern Ireland and Wales to scrap their present residency agreement, under which a player must have been educated in that country for five years under the age of 18.