The court ruled earlier Thursday that Puigdemont can be released on bail pending a decision on his extradition to Spain, saying the most serious accusation he faces there isn't punishable under German law.
Since October, Puigdemont had been living in Belgium.
The 55-year-old politician led a parliamentary session last year that saw separatist lawmakers vote for the region of Catalonia to declare independence from Spain.
The German judges still will consider approving his extradition on a lesser charge of misuse of public funds.
Puigdemont can leave prison as soon as he posts the bail, a court spokeswoman said on Thursday.
Judge Carmen Lamela said in an indictment that Mossos d'Esquadra chief Josep Lluis Trapero was part of an organized plan to seek Catalonia's secession, which courts have forbidden because the constitution says Spain is "indivisible". They said there was no indication he could be "exposed to the danger of political persecution".
Nevertheless, Puigdemont's defence team were "very happy for our client" that the "outrageous" charge of rebellion had been set aside, Dunckel said.
The Spanish government said on Thursday night that it respected the court's ruling on Mr Puigdemont's extradition. Puigdemont was imprisoned in Neumünster after being arrested at his entry to Germany through the border with Denmark, following an order given by the court of that city to keep him in prison and avoid his escape.
"We hope that we can arrange it so that by tomorrow morning he is a free man and can live in Germany in the following days and weeks", he said.
Spain's Supreme Court determined 25 Catalan leaders should be tried for rebellion, embezzlement or disobeying the state.
The Spanish government's quelling of the October 1 independence referendum drew global condemnation and outrage, with footage of national police officers and members of the Civil Guardia seizing ballot boxes and violently dispersing voters going viral on social media. Two other members of the regional police and an official with the regional interior department were also indicted.