He said the door had been opened to a unilateral declaration of independence.
Catalan officials later said 90% of those who voted backed independence in Sunday's vote. The turnout was 42.3%.
Spain's constitutional court had declared the poll illegal and hundreds of people were injured as police used force to try to block voting.
Officers seized ballot papers and boxes at polling stations.
"With this day of hope and suffering, the citizens of Catalonia have won the right to an independent state in the form a republic," Mr Puigdemont said in a televised address flanked by other senior Catalan leaders.
"My government, in the next few days will send the results of today's vote to the Catalan parliament, where the sovereignty of our people lies, so that it can act in accordance with the law of the referendum."
He said the European Union could no longer "continue to look the other way".