The former Leverkusen glovesman was expected to be his country's No.1 at the 2010 World Cup, but a string of injuries saw him lose his place in the Nationalelf, as his replacement Manuel Neuer went on to become Joachim Low's first choice between the sticks.
"I have enough ambition to think about playing for Germany again. I have to be successful at Hamburg first, though. Everything else will come automatically from there on," Adler told the official Bundesliga website.
"I feel as fit as a fiddle and I'm in tip-top condition. I was at Leverkusen for 12 years, and had a good time. But now I'm at HSV and I feel like it's my first day of school. A new experience is waiting for me.
"There is a new beginning to everything. I'm a man who likes to think in the long term, rather than one who likes to change clubs every season. I came to Hamburg to be a part of a new team."
Hamburg kick off the 2012-13 Bundesliga season with a home match against Nurnberg on August 24.