The 56-year-old spent five years at Stamford Bridge as chief scout but struggled initially in his role as the then manager, Jose Mourinho, reportedly did not want him in the post.
But he played a key role in bringing in players of the quality of Salomon Kalou, Florent Malouda and John Obi Mikel to the west London outfit, before deciding to jump ship and move to the Bundesliga outfit.
Hamburg are currently sixth in the German top-flight table but Arnesen is happy that he came and wants to help the club grow even stronger.
"Coming to Hamburg was a good decision for me. It has not always been easy, but I was not surprised that it was difficult." he told Bild.
"When I came we had nine players over 30 years old and we had to change that. We have young team that are on the right track. But the financial foundation needs to be stronger."