Manolete of AS reported Atletico won the race for Martins after he was one of the high-profile stars to ask that his Sporting CP contract be terminated after a group of the club's fans attacked players at a training facility in May.
Calciomercato.com said the Gunners and the Merseysiders were both interested in free-agent Martins, 23, while Italian club Lazio were believed to have tabled a contract worth €2.5 million (£2.2 million) per year.
Following Portugal No. 1 Rui Patricio's free transfer to Wolverhampton Wanderers earlier this summer, journalist Mark Rodden highlighted Martins as the next most valuable of Sporting's newly available stars:
Arsenal have seen Alexis Sanchez, Alex-Oxlade Chamberlain and Theo Walcott all leave the Emirates Stadium over the past year, with Henrikh Mkhitaryan the only presence arriving to help replenish the ranks out wide.
Meanwhile, Liverpool found themselves short on wide cover last term, and Martins could have been the ideal right-sided option to help offer Mohamed Salah competition on the flanks.
According to Manolete, the arrival of Martins will complete Atletico's offensive recruitments this summer. The wide man completed 2.6 dribbles per game in the Primeira Liga last term, per WhoScored.com, with only three players averaging more.
Writer Ben Hayward referred to the club's earlier capture of Thomas Lemar from AS Monaco, as well as the contract extensions of Antoine Griezmann and Lucas Hernandez, as cause for a successful transfer window:
One might have backed the more lucrative offers in the Premier League to win the race for an available star like Martins.
Football Radars illustrated the dribbling potency Martins brought to the table in the Primeira Liga last season, as well as the direct influence he had in getting the ball into dangerous areas:
Los Rojiblancos will offer Martins a new challenge in La Liga, while Arsenal and Liverpool could be forced to re-assess their options after missing out on what may have been a terrific bargain.