That day, Rajoy also sacked Puigdemont and all his ministers after the regional parliament declared independence following a referendum that wasn't sanctioned by Madrid and was banned by the courts. "The CUP will not block the formation of a new government", a statement by the party said.
Catalonia's parliament is expected to vote to approve a new leader of the region on Saturday.
Catalonia's parliament has failed to elect a regional president by absolute majority, in its fifth attempt to form a new government in the northern Spanish region.
Torra, 55, gave a combative speech during Saturday's debate. He has published several books about the history of Catalonia, according to the Catalan parliament website.
The announcement marks a major shift for Puigdemont after he declared Catalonia's independence past year, a move that prompted Madrid to intervene and dissolve parliament in favor of fresh elections. That prompted Madrid to impose direct rule and led to months of political limbo.
Mr Torra, vice-president of the activist group Omnium Cultural - whose leader, Jordi Cuixart, has been in preventative prison since October - is the so-called "Plan D" candidate after three previous inauguration attempts were blocked by the Spanish courts.
But since then, all candidates proposed by the separatist camp to lead Catalonia have fallen flat, as they are either overseas and wanted by Spain, or already in prison, charged with rebellion.
Catalonia has been in political limbo since December past year when pro-independence parties won early elections.
With the backing of Mr Puigdemont's Together for Catalonia (JxCat) coalition and the Catalan Republican Left (ERC), the success of Mr Torra's investiture bid is likely to hinge on the votes of the Popular Unity Candidacy (CUP).
"In contrast, Puigdemont's strategy is to continue using every opportunity.to continue challenging the Spanish authorities and keep the secessionist momentum alive".