Earlier this week, the lawyer of the politician said that he would give up his membership of the parliament, which would make it impossible for him to compete for the leadership of the government.
"Lawmaker Jordi Sanchez sent me a letter, in which he said he was refusing to present his candidature, with an understanding that this is the best that he can now do for the country," Torrent said at a press conference.
The president of the parliament added that on Thursday he would begin a new series of consultations on the candidates for the head of the government.
Torrent also criticized the refusal of the court to release Sanchez for the parliament session.
"His resignation should not have happened, but this decision is a testament to his honor," Torrent said.
Spanish Prime Minister Mariano Rajoy on Wednesday said that Catalonia should appoint a new head of the government as soon as possible.
On October 1, Catalonia held an independence referendum, which the central authorities did not recognize. After the regional parliament unilaterally announced independence later in October, based on the results of the vote, Madrid imposed the direct rule over the autonomous region and dissolved the Catalan parliament.
Former Catalan President Carles Puigdemont has refused to run for the position again, since he is unable to return to Spain, where he is facing arrest. Sanchez was arrested in October, alongside a number of other politicians, and accused of sedition.