Goal previously reported the midfielder would make the move after his country's World Cup campaign and with Uruguay falling to France in the quarter-finals on Friday, the path is now clear for Torreira to join the Gunners.
The midfielder, who made five appearances at the World Cup, confirmed he was set for a medical at Arsenal, denying him a chance to return to Montevideo with the rest of the Uruguay squad.
"I was very happy to leave for Uruguay with my team-mates," Torreira told Telenoche, "but this is a good opportunity and I don't want to waste it."
Torreira’s father Ricardo confirmed earlier this month that a programme is being prepared to help his son to settle in England once the transfer is completed.
"There will be people that will accompany him," he said.
"He won't be alone. It's a big change [going to England] and we don't want to think about it yet because we're scared.
"The truth is it's tough to manage the language, adapt to the [London] society and customs and at the same time not lose ours.
"But there's a whole programme getting readied for Lucas."
Torreira is set to join Stephan Lichtsteiner, Bernd Leno and Sokratis Papastathopoulos as off-season signings at Arsenal.
Sampdoria, meanwhile, have already prepared for Torreira’s departure by signing Czech Republic international midfielder Jakub Jankto, who had previously been linked with Arsenal, from Serie A rivals Udinese.