The Uruguayan completed his move to Diego Simeone’s side on deadline day, while the Gunners signed Thomas Partey after triggering his €50m (£45.3m) release clause with Atletico.
Fiorentina and Torino had also explored the possibility of signing Torreira earlier in the window.
But Torreira’s agent, Pablo Bentancur, has revealed that the midfielder was intent on joining Atletico and did not want to consider other options.
However, Atletico do not have a purchase option in their season-long loan deal for Torreira and could therefore be forced to pay a high price next summer if he impresses during his spell with Simeone.
‘Lucas’s operation was very complicated,’ Bentancur told Sport890.
‘We had other agreed-upon teams such as Roma, Fiorentina and Lazio, who play the Champions League, but Lucas was blunt. He told us that his goal was Atletico and that we get it for him and we work for the players.
‘They have agreed a loan for a year without a purchase option and the price is not defined, it will depend on his performance.
‘There is no option to buy because Arsenal had to pay the clause for Thomas.’