The three separatist politicians fled to Belgium in 2017 in order to avoid arrest on charges related to the Catalan independence referendum held on October 1 of that year, reports Xinhua news agency.
The Spanish Constitutional Court had ruled the referendum illegal.
Other former members of Puigdemont's regional government are still serving prison terms for their involvement.
In a vote held on Monday but made public on Tuesday, members of the European Parliament (MEPs) voted by 400 votes to 248 with 45 abstentions to lift Puigdemont's immunity, which means that Spain can reopen proceedings to request European arrest warrants for the three politicians on charges of sedition and the misuse of public funds.
Spanish authorities had sought to extradite them on charges of rebellion and sedition.
A previous request for an arrest warrant was rejected by Belgian courts in 2018 because charges of "rebellion" brought against the trio do not exist in Belgian law and the election of Puigdemont, Ponsati and Comin as MEPs in 2019 had given them immunity from prosecution.
Spain's Minister of Foreign Affairs, European Union and Cooperation, Arancha Gonzalez Laya, welcomed the vote that supported Madrid's view, saying that "Catalonia's problems will be resolved in Spain, not in Europe".
The decision showed that "an MEP can't use their position to avoid justice in their home country and demonstrates the solidity of the Spanish judicial system", she added.