The 66-year-old's future has come into question following England's early exit from the World Cup in Brazil.
However, after receiving the backing of the Football Association, Hodgson is eager to remain in charge of the side.
"With the backing of those around me and The FA I feel I am the right man to carry on," he told reporters on Sunday.
"This job means a lot to me. It is a fantastic job. I work with an incredible bunch of players, but we've got it all to do."
England play their final match at the World Cup on Tuesday when they face Costa Rica in Belo Horizonte.