Torreira, 22, becomes Arsenal’s fourth acquisition since Unai Emery was appointed as head coach in May.
The defensive midfielder has cost the Gunners a reported £27million and follows Stephan Lichtsteiner, Bernd Leno and Sokratis Papastathopoulos in joining the north London club this summer.
After narrowly avoiding relegation from the Premier League last season, Saints have bolstered their squad with the addition of Stuart Armstrong and Mohamed Elyounoussi.
Mark Hughes‘ side are still active in the transfer market, with a permanent deal for highly-rated City goalkeeper Gunn edging towards completion.
The 22-year-old impressed on loan at Norwich last term and was part of England’s World Cup training camp, having been involved with the senior team for the first time last November.
Southampton are also looking to bring in imposing defender Vestergaard from the Bundesliga.
Part of the Denmark squad that reached the last-16 in Russia, the 25-year-old would appear a timely addition to a side yet to bring in a defender since Virgil van Dijk’s world-record move to Liverpool.
Southampton’s only January signing was the club-record deal for Monaco striker Guido Carrillo – a player that has already been shipped out to Leganes on loan.
Dusan Tadic ended his four-year stint at St Mary’s to join Ajax, while questions remain over the future of Fraser Forster and Sofiane Boufal.
Former Spain striker Fernando Torres has announced he is joining Japanese side Sagan Tosu.
Torres was a free agent after leaving Atletico Madrid this summer and had been linked with moves to various leagues around the world.
It is Sagan Tosu who have won the race for his signature, though, with the 34-year-old revealing the J1 League to be his next destination at a promotional event on Tuesday morning.
The ex-Liverpool and Chelsea forward said in quotes reported by Marca: “We’ve had offers from all over. My new team will Sagan Tosu.
“Sagan Tosu were one of the first clubs to show an interest in me. They have convinced me with their sporting project.
“I think that Japan and the Japanese league is going to be a great experience.”
— サガン鳥栖公式 (@saganofficial17) July 10, 2018