The former England international says Hodgson has an advantage over Fabio Capello in leading the Three Lions.
Hill spoke to Goal Daily Podcast ahead of England's match against Ukraine in the final game of its group stage schedule, saying Hodgson adds the air of familiarity where former manager Fabio Capello did not.
Hill called upon Capello's lack of the mastery of the English language as a major part of his failure during his tenure, and the fact that Hodgson does not have a language barrier to contend with helps him.
"Hodgson has the touch to consolidate this team around. That you have to enjoy it - that's the key," Hill told Goal Daily. "I hope he's not going to be negative like I have seen him over the years but tell the players let's go out as Englishmen, not as players. Play the game you know."
Click here to listen to the full interview with Gordon Hill.