"I have made no secret of my wish to add Andy Johnson to my squad at Fulham and I am more than delighted that we have secured his services for the long term," Hodgson told the official Fulham website.
"He has all the qualities needed to assist us next season.
"There has been a lot of speculation regarding this transfer during the last week, very little of which has had any foundation.
"I am just happy to be able to focus on the positive news that Andy Johnson is now a Fulham player, one who we have great hopes for."