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.
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"Wayne realises what a good player he is. He will do everything he can to bring out the best in himself," Hodgson told reporters.
"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 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'. 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 is keen not to focus on the game entirely just yet.
"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."