The authorities in Madrid had been seeking Prof Ponsati on charges of "violent rebellion" and "misappropriation of public funds" over her role in Catalonia's controversial independence referendum a year ago.
Judge Pablo Llarena said in a decision published Thursday that he is revoking the worldwide arrest warrants against the six, in what the Catalan separatist movement was likely to regard as a major victory against Spain's central authorities.
On Thursday, Spanish judge Pablo Llarena withdrew the extradition requests after a German court ruled last week that Mr Puigdemont could not be sent back to Spain for rebellion, only for embezzlement connected to the alleged misuse of public funds for a referendum on secession.
Six other Catalan politicians are being held in custody on rebellion charges that carry a potential 30 year sentence.
Of those now overseas, Puigdemont and three others are charged with rebellion and other lesser offences like misuse of public funds.
Puigdemont's lawyer, Jaume Alonso-Cuevillas, declared triumph, writing on Twitter: "It looks like we have a memorable summer".
The revoking of the arrest warrants is expected to be viewed by Catalan separatists as a major victory against Spain's central authorities.
Germany rejected the rebellion charge because it requires an element of violence.
This means that Puigdemont, who was in Germany awaiting extradition proceedings, and five other Catalans who are scattered in Scotland, Belgium and Switzerland, are now free to move from country to country.
The decision meant that if he were to be extradited, Spain would only be able to try him on charges approved in the extradition order, and not rebellion.
A Spanish judge has now dropped the warrants for Ms Ponsati and other Catalan leaders who fled overseas.
"It's excellent news, with regards to my client Clara Ponsati, and obviously for Puigdemont. but we tread cautiously", lawyer Aamer Anwar told the Reuters news agency.