The West Bromwich Albion manager was the sole candidate approached for the job and met a four-man Football Association panel for around four hours on Monday for discussions that were described as "very positive".
A news conference was called for Tuesday afternoon after Hodgson had returned to Wembley.
Hodgson's current contract with his mid-table Premier League side expires at the end of June, meaning that the FA will not have to pay any compensation.
Neither Hodgson nor the FA made any official comment, although he was spotted leaving the Wembley headquarters on Monday evening with a copy of England's draft itinerary for Euro 2012.
The tournament in Poland and Ukraine, which starts next month, will be the new manager's first challenge.
Hodgson's impending appointment has divided opinion in England, with fans pleased to have an Englishman back in charge but Tottenham Hotspur manager Harry Redknapp the more popular choice with supporters and players.
"I like Roy, he's a top man and I'm sure he'll be a success," Redknapp said.
Dubbed 'Mr Average' by sections of the media, Hodgson commands respect for what he has achieved with less fashionable clubs, as well as his international standing and command of foreign languages, but no great measure of excitement.
"All the experience in the world that he'll have won't prepare him for this," he said of taking England to Euro 2012.
"The fans, the media, the players, the expectation of being the England manager is huge."
