The 23-year-old met up with his team-mates at Glasgow Airport on Thursday morning despite entering into talks with Blackpool at the weekend following their successful £500,000 bid.
Adam, who shone during a loan spell with the Championship club in the second half of last season, will be joined in Germany by his younger brother, goalkeeper Grant.
Andrew Shinnie, Andy Little and Alan Gow have also been promoted to the first-team squad while DaMarcus Beasley rejoins his team-mates following his extended break after competing for the US in the Confederations Cup.
Maurice Edu and Kirk Broadfoot will remain in Glasgow to continue their rehabilitation from knee and foot injuries respectively.
Meanwhile, Neil Alexander is not taking the goalkeeper's jersey for granted despite helping Rangers clinch the double last season.
The 31-year-old kept his place after Allan McGregor was suspended in April following his controversial behaviour on Scotland duty.
But Alexander knows he needs to keep proving to Walter Smith that he should be first choice.
The former Cardiff and Ipswich player said: "I think the gaffer will take everything into consideration when he makes his decision but of course I'd be disappointed if I didn't start with the way things happened last season.
"But I've got to keep an open mind, I did join Rangers as a number two and Allan was the established number one and maybe still is.
"Being a number two, I've maybe been fortunate in the last two
seasons to get as many games as I have because I could quite easily have come and not had one first-team appearance.
"I've been very fortunate the way things have happened but Allan is still probably regarded as the first choice goalkeeper and I'm his number two.
"Having said all that, it's up to me to prove to the manager that I can still come in and beat the number one."