Torreira will wear the number 11 shirt vacated by midfielder Mesut Ozil.
"In Lucas Torreira, we have signed a young player who is a very bright talent in the game", said Emery.
"He has big potential and gained good first-team experience last season with Lorient". I want to become part of the club's history and to achieve great things.
Click through the gallery above to see Arsenal's signings in this window so far.
Revealed Which Shirt Number Will Lucas Torreira Wear At Arsenal Posted by Daniel Jenkins
Guendouzi joins Uruguayan global midfielder Lucas Torreira, veteran Swiss defender Stephan Lichtsteiner, German goalkeeper Bernd Leno and experienced Greek defender Sokratis Papastathopouloss as new arrivals at the Gunners.
"I feel very happy", Torreira said after the announcement was made.
NAIJ.com previously reported that Arsenal have announced their first signing of 2018 hours after an engaging 2 -2 draw at home to Chelsea and it is Greek defender Konstantinos Mavropanos.
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. He returned to Sampdoria before the 2016/17 season and during his time with "La Samp" made 71 appearances, becoming a first-team regular and an integral part of the side.
The 19-year-old Lorient midfielder was expected to undergo his medical on Monday and his arrival could be announced later in the week.