Eriksson, who led England from 2001 to 2006, has known Hodgson for more than 30 years.
"He is very organised, knows his football and has been successful in many countries," Eriksson told BBC Sport.
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"He will do a very good job, I am sure. Back him up and help him."
The duo's friendship began in the late 1970s, when they were both managers in the Swedish league. Eriksson was at Degerfors, while Hodgson was in charge of their rivals Halmstads.
And in the 1990s they again faced each other, in Italy's Serie A, when Eriksson was at Sampdoria and Hodgson at Inter Milan.
"I have known Roy very well for many years, I am a friend of his," Eriksson said. "Tomorrow I will phone him to congratulate him."
And Eriksson strongly disagrees with accusations Hodgson does not have a big enough personality to be England manager.
"I don't think that's fair," he said. "He is a good man and has charisma, of course he has."
He also disputed claims Hodgson had failed in his two most high-profile jobs, at Inter Milan and Liverpool.
"Liverpool, I don't know what happened there," he said. "And at Inter, they had him back for a second spell at the club, so he can't have done a bad job."
The Swede said Hodgson would just have to accept he could not please all sections of the media and fans all the time.
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"It's always like that, isn't it?" he said. "When I took that job, I wasn't English and some people never accepted that. But why shouldn't people be behind him at the start?
The 64-year-old admits he had originally expected Harry Redknapp to get the England job, but is confident Hodgson has the attributes to succeed.
"When I think about it, it's actually not a surprise," he said. "Roy is English and has huge experience of international football. I think it is a very good choice.
"West Brom have been doing extremely well under him and he will try to play good football with England, of course.
"He is starting a little bit more than a month before the Euros start and shouldn't be judged on that tournament, although I am sure England can do well there under Roy."
Sven-Goran Eriksson has urged fans to back his friend Roy Hodgson, insisting he will a big success as England manager.