Roma boss Claudio Ranieri said: "Stefano is a great lad. He has been at Roma for five years and I believe the experience in England could mark a turning point in his career.
"He can do a lot more and the Premier League will give us back a much stronger player."
Okaka made his first-team debut for Roma in 2005 and scored his first goal for the club in September 2006.
The forward, who was loaned out to Modena and Brescia last season, said: "I have grown thanks to the advice of my team-mates, but to have a leap in quality, it is crucial for me to go to England and play in the Premier League.
"I hope I can return stronger than before."
Okaka completed a medical last week and Hodgson revealed the club had been monitoring the striker long before his the clubs met in Europe.
"We've monitored him for a long time, before we were drawn against Roma in Europe," said Hodgson, who has been keen to boost his strikeforce following injuries to Andy Johnson and Clint Dempsey.
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