Hodgson is on a visit to Manaus, where England face Italy in their opening game at the Arena Amazonia, but there are fears an unfinished stadium in Curitiba could be pulled.
"Fifa and the Brazilian government has put in a lot of work," Hodgson said.
"So I don't see any reasons for us technicians to doubt them."
A potential repeat of the violent protests that dogged the Confederations Cup is a concern for organisers, but Hodgson said he had faith in the local organising committee.
The Arena Amazonia, like five other World Cup venues, was not ready by the Fifa deadline of 31 December 2013.
But Fifa secretary-general Jerome Valcke declared he was happy with the stadium in a visit over the weekend, and officials say it is 97% complete.
The World Cup begins in Brazil on 12 June, but the Sao Paulo venue due to stage the opening match is one of the sites still under construction.
Fifa is known to be exploring alternatives to Curitiba should its Arena da Baixada stadium fail to be completed on time, and Valcke said a final decision on the city's involvement would be made on Tuesday.
England's first Group D game is against Italy on 14 June and Hodgson visited the 42,000-capacity venue as part of his trip, which also included a boat ride up the Amazon river and a visit to the city's 130-year-old Royal Opera House.
From now until during the World Cup, temperatures can rise above 30C in Manaus, and its proximity to the Amazon rainforest means humidity levels hit over 95%.
The Football Association has made extensive preparations to ensure England's players are able to cope with the conditions and, having also managed Switzerland in the sweltering heat of the 1994 World Cup in the United States, Hodgson wanted to experience the conditions before his squad arrives in June.
"It is hot here, but World Cups are played in the summer," the 66-year-old told BBC Sport.
"It was hot in South Africa [for the 2010 World Cup] and it was very hot in America in '94.
"It will be hot here but that is something you have to come to terms with. What we are interested in now is getting a feel for the slightly more different, more tropical climate in the north of Brazil vis-a-vis Rio, where we have been and played."
England will base themselves in the more temperate climes of Rio de Janeiro, and their other two group matches against Uruguay and Costa Rica will take place in Sao Paulo and Belo Horizonte, which also enjoy more moderate conditions.
Hodgson caused anger prior to the World Cup draw when he said the conditions in Manaus made it "ideally a place to avoid".
City mayor Arthur Virgilio Neto initially said England were not welcome, but an apologetic letter from Hodgson smoothed things over to the point where the Brazilian official was happy to receive the England manager and his delegation on Monday.
"It was a simple misunderstanding," Neto said when asked about his angry reaction to Hodgson's comments.
"We respect England, we respect the English team. Personally, I admire Wayne Rooney a lot."
Before heading to Manaus, Hodgson visited Miami, where England will play two friendlies during a pre-World Cup training camp.
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