The move created "roster relief and flexibility for the rest of the 2020 season," vice president and technical director Carlos Bocanegra said in a statement.
As a result, Martinez, who underwent surgery in March to repair a torn ACL in his right knee, cannot play in any of Atlanta's games this season.
Bocanegra assured the 27-year-old's rehabilitation program is still going to plan, playing down fears he had suffered a setback in his recovery.
Atlanta was eliminated from the MLS is Back Tournament without scoring a single goal. MLS is expected to schedule regular-season games after the tournament concludes in Orlando on Aug. 11.
Torres returns to MLS after two difficult years in Mexico's Liga MX. He scored just nine goals in 45 appearances across all competitions with Pumas and Club Tijuana.
Torres came through the academy at Chivas Guadalajara and joined the club's MLS affiliate on loan in 2013. He also spent parts of two seasons with Houston, recording 14 goals as the team's leading scorer during the 2017 campaign.
"Cubo is a natural goal-scoring forward who will bolster our front line, and we're pleased to add a player of his quality to the team," Bocanegra added. "He has consistently shown his finishing abilities in MLS, Liga MX and on the international stage, and we expect him to immediately contribute to the second half of our season."