The Arsenal winger's participation in the global showpiece was placed into doubt when he suffered knee ligament damage in a friendly against Ecuador on Wednesday.
However, Hodgson offered a positive update on the 20-year-old's condition after seeing England draw 0-0 with Honduras on Saturday.
"Alex Oxlade-Chamberlain is making good progress - I think he'll make the tournament without a shadow of a doubt," said Hodgson.
After taking on Ecuador and Honduras in Miami, England have six days to go until their World Cup opener against Italy in Manaus.
Prior to his team's departure for Brazil, Hodgson added: "We're really looking forward to the tournament and have fortunately not suffered more than the one injury to Alex.
"I really think that where we've based our training camps – first in Portugal and then at St George's Park, then with a game at Wembley and two in Miami – couldn't have worked much better for us and we go to Brazil in a very good frame of mind."
