Hodgson, appointed on May 1 to replace Fabio Capello who quit in February after guiding England to the finals in Poland and Ukraine, also named Liverpool striker Andy Carroll in a 23-man party along with uncapped Norwich City goalkeeper John Ruddy and Arsenal's teenage winger Alex Oxlade-Chamberlain.
Striker Wayne Rooney was included despite having to miss the first two matches of the tournament through suspension, while Liverpool midfielder Steven Gerrard will captain the side who have been drawn in Group D with co-hosts Ukraine, France and Sweden.
Defender Terry is in the squad despite losing the England captaincy in February after being sent to a trial on July 9 charged with racially abusing Queens Park Rangers defender and Ferdinand's brother Anton. He has pleaded not guilty.
"I realised when I selected him there would be people who would raise their eyebrows, that's the decision I have made and the decision I will live with," Hodgson told a news conference at Wembley stadium on Wednesday.
"I believe that John Terry, especially in the latter half of the season, has played very well. I selected him because he is the man for the job."
"Rio is a man who I respect as a player, and as a person. I don't know him well personally but I've seen enough of him over the years to realise what a fine footballer he is, what a good person he is," added Hodgson.
"But I had to make a footballing decision, had to decide on the basis, basically, of what I have seen in recent months, in particular, influenced to a certain extent by the fact that Rio hasn't played so much since the [2010] World Cup and has only played for England once in the last year."
Ferdinand, 33, said he was "gutted" by the snub.
"Absolutely loved playing for England. To say I'm gutted is an understatement of the highest order," he wrote on Twitter.
Gerrard was the man to help forge "team unity", Hodgson said, adding that the player he knew well from his time as Liverpool manager merited the "distinction" of captaining England.
Gerrard's Liverpool team-mate Carroll got the nod up front ahead of Stoke City's beanpole front-man Peter Crouch, who boasts a fine scoring record at international level with 22 goals in 42 appearances.
"He [Carroll] is a different type of player to the others in the squad," said Hodgson. "He has that ability to hold the ball up, that aerial ability which is very useful, but also has the ability to make runs behind defenders and use his strength and his power."
"It hasn't sunk in yet but I'm absolutely over the moon," he told Sky Sports. "It was quite surreal. I can't wait to get started. It just caps off a wonderful couple of years I've had at Norwich."
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