According to SPORT, the Argentina forward informed Atletico sporting director Mateu Alemany that he would stay at the Metropolitano until at least the January transfer window.
The decision brings an end to a complicated European summer for Alvarez, who attracted interest from several clubs but reportedly made Barcelona his preferred destination.
Arsenal were among the clubs seriously interested in signing the 26-year-old, but a move to the Premier League did not appeal to Alvarez in the same way as a switch to the Catalan giants.
Barcelona also made no secret of their admiration for the forward, with club president Joan Laporta publicly discussing their interest. However, Atletico were unwilling to negotiate a sale with their La Liga rivals.
Atletico's board maintained its position throughout the transfer saga, with chief executive Miguel Angel Gil Marin making it clear that the club did not want to sell Alvarez to Barcelona.
With no agreement possible, Alvarez has chosen to remain and continue working under Atletico manager Diego Simeone rather than leave Madrid for a club he did not consider his preferred option.
Barcelona have strengthened their attacking options by signing Gabriel Jesus, but that does not necessarily end their interest in Alvarez.
The Argentine remains highly regarded at Barcelona, and his reported desire to eventually play for the club could keep the transfer story alive.
