The Spanish government made its decision a day after a judge granted Yalcin provisional release without bail.
"I was really pleased when I received the news," the writer told Swedish news agency TT. "This felt completely unbelievable just a day ago."
Yalcin, aged 59, is a Swedish-Turkish dual citizen and writer for online magazine Odak. He was held by Spain on Turkey's orders after being arrested on August 3rd at Barcelona's El Prat airport, based on allegations of insulting Turkish President Recep Tayyip Erdogan and "supporting terror groups".
Human rights campaigners insist the detention was designed to silence political dissent in a crackdown under the state of emergency imposed in Turkey after last year's coup attempt. Yalcin writes for a left-wing online magazine critical of the government in Ankara.
He is now looking into the possibility of claiming damages from the Spanish state over his imprisonment.
"If I can, I'll do it, but I haven't spoken to my lawyer yet and don't know if it's possible," he told TT.
Yalcin said that his detention "put a mark on me and my work – many people think that if you are sought by Interpol, there must be a reason for that".
The Swede has been represented by Spanish human rights lawyer Baltasar Garzón, who said that Friday's decision meant Yalcin is safe at least as long as he stays within the EU.
"It is theoretically possible that Turkey could request his extradition if he travels to a country outside the EU –but I find that far-fetched," he said. "We will work further to ensure that Interpol's 'red flagging' of him is also removed."
Swedish Foreign Minister Margot Wallström also commented on Yalcin's release, writing in a statement published on the government website: "I welcome the Spanish decision not to extradite Hamza Yalcin to Turkey. Hamza Yalcin is now free to travel and can see his family again."