The Manchester United striker missed the final three games of the Premier League season with the problem but has trained in Portugal over the past week.
He was not involved in shooting drills in Vale do Lobo on Wednesday, but Hodgson has been impressed with his commitment.
The former Liverpool boss backed the 28-year-old to produce a strong performance in Brazil, having suffered with fitness problems in the build-up to the FIFA World Cups in 2006 and 2010.
"Wayne realises what a good player he is. He will do everything he can to bring out the best in himself," Hodgson said.
"The eyes of England, if not the world, are on him and he'll do everything he can to bring out his best qualities.
"He spent the previous week at his villa in Portugal but he trained all through that week to make sure he is over his injury.
"He said to me, 'When you arrive on Monday I want to be 100 per cent ready to train on the first day'.
"He was disappointed to be left out of the training session (on Wednesday) because I wanted to protect his thigh.
"If it was up to him he would have trained."
Hodgson's men will face Peru, Ecuador and Honduras in preparation for their Group D opener against Italy on June 14.
But the ex-Inter coach is not yet ready to focus entirely on that game in Manaus.
"Italy is still three weeks off. It's much too early to concern ourselves with that now," he continued.
"It's very much in our minds but (not in terms of) video preparation and tactics.
"All I know is, having worked in Italy, that they will be under pressure and scrutiny.
"Everyone in Italy will be expecting them to beat us. But there won't be many coaches who go into the World Cup without pressure.
"Anything I read about other teams I take with a pinch of salt."
