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.
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."
