Spanish Prime Minister Mariano Rajoy ordered the December 21 regional election under constitutional powers he invoked in October to dissolve the previous parliament after separatist lawmakers voted to declare Catalonia an independent republic.
Differences between the two have grown since Puigdemont led separatist lawmakers in unilaterally declaring Catalan independence from Spain on October 27.
Prime Minister Mariano Rajoy called an election in Catalonia on 21 December to try to resolve Spain's worst political crisis in decades after Catalan leaders declared independence in October following a banned referendum on secession.
However, the party that won the most votes, which supports the unity with Spain, poured scorn on the plan as Puigdemont is in self-imposed exile in Brussels and would be a "hologram president".
Under the agreement between Mr Puigdemont's Junts per Catalunya party (Together for Catalonia) and the Catalan Republic Left, the fugitive politician would be installed at a meeting of the parliament next week.
Market-friendly Ciudadanos, which wants Catalonia to remain part of Spain and is led by Ines Arrimadas, gained the largest share of the popular vote but unionist parties did not win enough seats to govern by majority.
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The deal - reached over dinner in Brussels on Tuesday - would allow Puigdemont to deliver his acceptance speech this month either by videoconference from Belgium or by having another lawmaker read it in the Catalan Parliament on his behalf, according to the Catalan radio station Rac1 and other outlets.
Carles Puigdemont aims to return to office as president of Catalonia - despite the fact it's unlikely he'll actually return there in person. Puigdemont became the independence movement's leader but is now a fugitive in Belgium.
Many of the Catalan political leaders were arrested on charges of sedition and rebellion after the independence declaration.
The parties' announcement Wednesday raises the specter of a renewed push for independence - and also raises hard questions about how, exactly, Puigdemont might go about governing.
In an editorial published on the Politico news website on Wednesday, Puigdemont reiterated his call for talks with Madrid, which Rajoy has tentatively agreed to but on condition that the region drop its push for independence. Spain has jailed other pro-separatist leaders involved in the independence push.