Hamburg win race for Elia
The 22-year-old former Den Haag front-man netted 11 league goals in 64 appearances for ex-England boss Steve McClaren's side since arriving in 2007, and impressed in Twente's UEFA Cup tie with Manchester City last season.
His form had led to reported interest in the youngster's services from Mark Hughes' Blues, as well as Everton, Spurs, Bayern Munich and Ajax.
However, Elia has opted to snub all of them in favour of a move to Hamburg, who have agreed a fee in the region of €9million.
"I am very happy it's worked out. HSV is a fantastic club that is playing a major role in Germany," he told Algemeen Dagblad.
"I want to thank Twente and [chairman] Joop Munsterman for making this transfer possible.
"I am also very thankful to the club for the chances I got the last two seasons. Thanks to Twente I have made it to the Dutch national team.
"At HSV I hope to take a new step in my development and hope to stay in the Dutch squad ahead of the World Cup. My dream is to play in South Africa in 2010."