Puigdemont's announcement from exile in Germany came a day after the Madrid government stepped in to block him from once again becoming president of Catalonia, pressuring the separatist camp to pick another candidate and form a regional government.
Separatist allies had said they would try to have Puigdemont back in the role by next week after the regional parliament voted through reforms allowing him to be re-appointed without being present.
Madrid, however, successfully requested the Constitutional Court to cancel the reform and in a video message Puigdemont said he was now willing to step aside.
"The intolerance and the lack of respect of the state towards the will of the citizens of Catalonia have appeared clearly in the eyes of the world," he said in the video.
He proposed political newcomer Quim Torra as his successor, urging the next regional executive to build an independent country.
The region has been in political limbo since Spain's conservative central government imposed direct rule on the region after it unilaterally declared independence in October.
Separatists won regional elections in December, but fresh polls will be triggered if a new leader is not elected by May 22nd.
Puigdemont, who first fled to Belgium, was detained in Germany in March after Spain issued a European arrest warrant against him.
Madrid wants to extradite him to Spain to try him on charges of rebellion and misuse of public funds for staging an independence referendum in Catalonia on October 1st even though the courts had ruled it unconstitutional.
A German court last month dismissed the extradition request for Puigdemont on the rebellion allegations and released him on bail.
Spanish prosecutors have since handed over new information to Germany they hope will prove the use of violence, to justify the rebellion charge and their extradition request.
Only last month, hundreds of thousands of people marched in Barcelona to protest the jailing of nine Catalan separatist leaders who are facing trial on "rebellion" charges in Spain.
The protest came six months after the first incarcerations of the leaders for misuse of public funds, sedition and rebellion -- which carries a prison sentence of 30 years and implies that a "violent uprising" took place -- over their separatist push.
They include the heads of Catalonia's two largest pro-independence groups -- Jordi Sanchez of the ANC and Jordi Cuixart of Omnium Jordi Cuixart.
Prosecutors say the two men played central roles in orchestrating pro-independence protests in September in Barcelona during which national police were trapped inside a government building for several hours and their
vehicles were destroyed.
They are also accused of mobilising thousands of pro-independence supporters to prevent police from stopping the October 1st independence referendum from going ahead.
Sanchez was elected as a lawmaker in snap polls in Catalonia in December and has twice been proposed as a candidate to lead a new Catalan regional government, but a judge refused both times to allow him to leave jail to be sworn in.