"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," added Hodgson.
"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."
Johnson is Fulham's 11th signing since they clinched Premier League survival on the final day of last season and he is likely to form a new strike partnership with Bobby Zamora, who arrived from West Ham in July.
The fee for the former Birmingham City striker should enable Everton manager David Moyes to make a second bid for Sporting Lisbon midfielder Joao Moutinho.
Moyes had an initial £11.8m offer rejected by the Portuguese club, with Sporting not keen on selling the 21-year-old for less than £20m.
Everton have yet to make a signing this summer and Moyes has conceded he may need as many as five or six new players.
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