Despite the withdrawal, the judge said they still faced possible charges for sedition and rebellion.
Rebellion is considered one of the most serious crimes in Spain, carrying a jail term of up to 30 years.
Spanish Supreme Court judge, Pablo Llareno, announced the move on Tuesday, citing willingness the former Catalan President's had shown to return to Spain ahead of fresh regional elections.
The five were fighting extradition back to Spain, saying they could not be guaranteed a fair trial on their return.
Campaigning has now officially started ahead of the 21 December vote moved forward by Spanish authorities.
Speaking from a video-link from Belgium on Monday night, Mr Puigdemont said the new vote was a choice between "nation or submission".
"They can choose between Catalan institutions or dark characters in Madrid," he said.
All but one of the 13 leaders sacked by the Spanish government are standing for election again in the fresh vote.
On Monday six ministers being held in a prison near Madrid were released from prison on bail. Two others, including the former Catalan vice-president, remain in custody.
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