In an exclusive interview with Sampdorianews.net, Betancourt explained that Arsenal were able to see off competition because of an agreement they reached early on in the transfer window.
The agent stated: "Lucas was also requested by Borussia Dortmund, Naples and some Spanish teams, but there was a word agreement with Arsenal, everything was closed even at the club level."
Betancourt went on to state that he is certain Arsenal are the right club to help his client develop, praising new manager Unai Emery.
He added: "I am convinced that Arsenal is currently the ideal team to continue the path of growth. Emery immediately had words of great appreciation towards him."
Torreira featured in all five games for Uruguay at the World Cup and impressed in each of his appearances. The midfielder also held a regular starting place in Sampdoria's side, making 71 appearances in two seasons.
Emery has moved quickly in the transfer market as he looks to improve Arsenal's leaky defence, which conceded 51 goals last season. The signings of Sokratis and Bernd Leno, in addition to Torreira, appear to have bolstered the defence of the Gunners, who will be aiming to qualify for the Champions League this season.