Hodgson, whose own spell ended after a shock 2-1 defeat to Iceland at Euro 2016 this summer, believes that the team still has a lot of potential and hopes that Southgate will help them to reach a new level.
"I endorse the appointment the same way as everyone else has. It's great that he comes into the job with such a positive perception of him as a person, him as a coach, and his experience of the FA and what he's capable of doing," he told Sky Sports News.
"I think the team's very good, I think we have good players, I think they know what they're doing. I think that they're dangerous going forward, there's a lot of players who are very dangerous, who can cause all opposition problems, but most important of all they are strong defensively, they get back quickly, they have the five-yard furies, they win the ball back quickly in the Barcelona manner.
"These are all things I think which make for a good football team. If Gareth, as I believe has happened so far, can keep a good atmosphere, can keep the players wanting to play for England, wanting to continue to improve, I can only see a very positive future."
Hodgson also outlined his desire to return to management at the age of 69.