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.
Newspapers reported that the 64-year-old was likely to be offered a contract taking him through to at least the 2014 World Cup finals in Brazil and probably Euro 2016.
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.
The FA said on Sunday that West Brom had granted permission for them to speak to Hodgson about a role that has been vacant since Italian Capello quit in February.
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.
Redknapp said on Monday that he bore no grudges at being overlooked and wished the former Switzerland, Finland and United Arab Emirates coach all the best.
"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.
He was sacked after 18 months as manager of Blackburn Rovers and just six months after taking the helm at Liverpool.
Former England international defender Gary Neville said the man who took Fulham to the Europa League final and also coached Inter Milan in Italy, would face a big test in the next few months.
"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."
