"The deal is on. It was never really off but there have been a lot of problems to iron out," said Hodgson.
"At the moment he's finishing off a medical. Barring any problems with the medical I expect him to join us from Monday.
Okaka started both of this season's Europa League matches between the clubs and scored the winner at the Stadio Olimpico in early November.
"Okaka played against us and did well. He's also played for Italy Under-21s," said Hodgson.
"We've been monitoring him for a long time, before we were drawn against Roma in the Europa League. His name was well known to our scouting staff."