Arsenal are understood to have agreed a £26.4million deal to land Torreira this summer but the Gunners have had to wait to complete the signing of the 22-year-old midfielder.
Torreira confirmed that he chose to delay his medical until after Uruguays participation in Russia and it appears the Sampdoria man is on his way to north London imminently.
An official statement from Uruguays FA revealed that Torreira was not on the flight with the rest of his team-mates as they headed back to Montevideo following a 2-0 defeat to France.
A charter flight will return 17 of the 23 players that make up the squad. Carlos Sanchez, Lucas Torreira, Gaston Silva, Martin Silva, Cristhian Stuani and Rodrigo Bentancur will not return with the delegation, the statement read.
Arsenal have already signed Stephan Lichtsteiner, Sokratis Papastathopoulos and Bernd Leno and its expected that Torreira will be unveiled next week.
Torreira hailed Uruguays magnificent World Cup campaign after their defeat to France in Nizhny Novgorod.
Being part of this squad in this World Cup, the truth that it was something magnificent, he said.
We go home with our heads held high because we knew how to leave everything until the end.
Asked if he postponed his medical with Arsenal until after the World Cup, Torreira responded: Yes, we could have done things differently, but I did not want to think about other things.
The World Cup is important and being part of this squad meant a lot to me.
But now I have more time my future will be very clear.
The important thing is that Im happy to have been part of this squad and this World Cup, so I thank all the people who accompanied us.