Oxlade-Chamberlain picked up the injury in Wednesday's 2-2 draw with Ecuador and Hodgson had said he may have to wait until 24 hours before England's Group D opener against Italy on June 14 before deciding whether the Arsenal wide-man could be part of his squad.
But yesterday Hodgson took a much more positive tone.
"Everyone is fit. Oxlade-Chamberlain is making good progress. I think he'll make the tournament without a shadow of a doubt," Hodgson said.
Captain Steven Gerrard was replaced at half-time but said that had been planned before the game due to a slight concern over his groin after Wednesday's game.
"I had a tight groin in midweek so it was always the plan for me to play just 45 minutes. We're quite frustrated in the dressing room. We thought the referee was poor, they were doing some stupid fouls.
"Maybe we could have moved the ball a bit quicker, but there were some horrific challenges. I certainly got caught by one," he said.
"Honduras were quite physical," said Hodgson, "It was a real stop-start game, one of the most frustrating I've been involved in for a long time. We had a long stoppage, I thought we dealt with it and in the second half it was attack versus defence.
"But now it is time for the real thing," he said before England headed off to the airport to catch their flight to Brazil.
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