The Nerazzurri have sent their best wishes to the 64-year-old, who previously had two spells as coach of the Italian giants, after he was announced as Fabio Capello's successor
The Englishman enjoyed two previous spells in charge of the Nerazzurri in the 1990s and leaves West Bromwich Albion to take charge of the Three Lions.
“It is with great honesty and happiness that president Massimo Moratti and all the Nerazzurri family celebrate the nomination of Roy Hodgson as manager of England,” read the statement.
“The Football Association’s choice is the most prestigious prize for an English manager, but in this case rewards a person who has always shown honesty and generosity towards Inter, qualities that formed a rapport of true friendship.”
Hodgson's first game in charge of England will be on May 26 when he takes his team to Oslo to face Norway in a friendly.