Spanish publication AS claim Martins has agreed to join the La Liga side and will complete the transfer in the coming days.
Arsenal were among the clubs hoping to snap up Martins on a free transfer after he moved to cancel his Sporting Lisbon contract.
Unai Emery has a limited transfer budget this summer after Arsenal failed to qualify for the Champions League for a second year in a row.
He has already gone about reshaping his squad but fancied Martins to bolster his attack.
The Portugal winger, 23, requested his Sporting contract was ripped up on June 11 after the incident which saw supporters invade and attack players at the training ground.
Arsenal transfer news: Gelson Martins is set to join Atletico Madrid
Arsenal transfer news: Gelson Martins has agreed to join Atletico Madrid
Martins was with Portugal at the World Cup and was sent home from Russia by Uruguay last Saturday.
Arsenal have made defensive signings their priority so far this summer with goalkeeper Bernd Leno, and defenders Sokratis Papastathopoulos and Stephan Lichtsteiner coming in.
Uruguay midfielder Lucas Torreira is expected to make the move when his World Cup is over.
But Emery will have to look for another winger to bring in if he still wants to add in that area with Martins now set for Atletico Madrid.
Arsenal have been linked with Argentina youngster Cristian Pavon, but AS claim it will take a bid of £44m to sign him from Boca Juniors.
Arsenal lost Alexis Sanchez in January but did bring in Henrikh Mkhitaryan from Manchester United as part of the deal.
He will compete for an attacking slot with the likes of Mesut Ozil, Alexandre Lacazette, Pierre-Emerick Aubameyang, Alex Iwobi but Emery still wants more options for the wide roles.