Mr Puigdemont's Together for Catalonia party claimed 34 seats, while the other two pro-independence parties won a combined 36.
That total gives separatists two more seats than the 68 needed for an absolute majority - ensuring that they retain control of Catalonia's regional government.
Despite this, unionist party Citizens topped the poll and won 37 seats.
Catalonia went to the polls after its government was dissolved by Madrid who deemed its declaration of independence in October "illegal".
Mr Puigdemont says Thursday's majority by separatist parties was a victory for the "Catalan republic" over the Spanish state, and said Spanish Prime Minister Mariano Rajoy and his allies "have lost".
The ousted Catalan leader was speaking from Brussels, where he went into self-imposed exile after his government was sacked by Mr Rajoy when he declared independence from Spain.
"This is a result which no one can dispute," Mr Puigdemont told supporters in Brussels.
"I think we have earned our right to be listened to."
Mr Puigdemont said it was "a slap" for the Spanish PM, adding: "Rajoy has lost the mandate he sought."
The leader of the pro-Spanish party that won the most votes promised her party will continue to fight the region's separatists.
"The pro-secession forces can never again claim they speak for all of Catalonia," Ines Arrimadas said.
"We are going to keep fighting for a peaceful co-existence, common sense and for a Catalonia for all Catalans."
"Today we have sent a message to the world, that the majority of Catalans feel Catalan, Spanish and European and will continue to do so," she added.