A fee has been settled between the two clubs, the Gunners agreeing to go to €30m to sign the Uruguay international - a clear €4m more than his contract's buyout clause.
Arsenal's eagerness to get a deal done quickly is no surprise to those who have worked with Torreira throughout the 22 year-old's burgeoning career. Here's just what some identities from Italian and Uruguayan football have said about the midfield schemer:
MASSIMO ODDO (ex-Pescara coach): "It was during the preseason, the club told me to evaluate him and if not, Torreira would have been sent back to Uruguay. He had personality, physical strength ... but he always wanted to have the ball at his feet, so I told him: 'Why don't you play as a defensive midfielder and not as a playmaker?' And I kept him in the first team."
MARCO GIAMPAOLO (Sampdoria coach): "If Torreira was 1.80m tall, he would already cost €100 million and would be considered one of the strongest directors in the world. He can play short or long, he wins the challenges, plays and always seems to understand in advance where the ball will go.
"He will go to a big club that will not pay attention to his stature.
"He's strong, complete, awake, intuitive, he has a great personality."
ROBERTO DRUDA (Pescara scout): "Giorgio Repetto (ex-Pescara director general) has discovered (Marco) Verratti, he like Oddo and many others was convinced that Torreira could be even stronger than Verratti.
"The only doubt is that everyone believes he's small, but have you seen how he outplayed (AC Milan midfielder Franck) Kessie? The athletic trainers always say it: muscularly he is very strong.
"Torreira's height has always put doubts in a footballer that is never so physical, but then you have seen this player has gone so far as to remove any doubt."
RICARDO TORREIRA (father): "We are looking for the best solution for Lucas, at the moment there are various teams on him but we have discarded the possibility of Napoli.
"Because? It's a talk to do with the entourage of my son, I do not know why but at the moment it is a hypothesis to be rejected. My dream is to see my son in the team where he wants to play. I am happy with what my son is doing in Serie A, we are all happy."
CARLO OSTI (Sampdoria director general): "Torreira has gone from Serie B to A with a paltry ease. It was said: if only he scored some goals, he would be perfect. He has already scored three and on Monday my phone has rung constantly. No one will leave in January. But they are already asking me everything about him."
LUIS SUAREZ (Barcelona striker): "One day we played against Sampdoria, and I was surprised by that little boy who had been there in the middle for the whole game. After that evening I learned that he was Uruguayan, and from that moment on I started to follow him a bit in Serie A.
"He has surprised me and improved a lot. He arrived very young in which it is not easy to assert himself, but he also managed to obtain a high level performance.
"Have him in the national team? Obviously, the choices about are up to coach (Oscar) Tabarez but, if there were the possibility, he would be welcome. I'm sure he would make the most of the opportunity."
OSCAR TABAREZ (Uruguay coach): "There is an atmosphere as if the media have discovered Torreira and I am laughing. It seems that one had not done anything until now and this is all a surprise. A year ago we were following him, just as Matías Vecino was followed two years before calling him. That's because we call them when they're ready.
"Torreira, in statements he made, told his story and said he was here in a youth team. I read that he said he was a left winger. And he said that Massimo Oddo, his coach at Pescara, told him to play in a position similar to now. And he also said that now with many tactical improvements he's better equipped.
"When a player exceeds those demands to play at a level as important as the Italian league, the Spanish, the Premier League, the French or the German, he can play any international game."
MASSIMO FERRERO (Sampdoria president): "I do not need to sell, the boy is fine with me. The market is a bit distorted. We gave (Milan) Skriniar to Inter, Juventus received €100 million for (Paul) Pogba, but if Torreira was with Juventus and the Bianconeri had sold for €100 million nobody would have said anything.
"If for Torreira I sell him for double I cause a sensation because we are Samp, if Napoli does it, then nobody talks.
"If your wife wants to go with one with blue eyes, what are you doing? You cannot do anything. It's another thing we'll have to discuss, if a player has in his head to go somewhere else, we as a club cannot do anything."
PABLO BENTANCUR (agent): "Many clubs have called for him, he is a player of great heart and quality, give the coach, Marco Giampaolo, credit for having made him grow and established.
"We'll try to find a solution for Lucas, otherwise we'll look around. But I will not speak to the president through the newspapers."