The 23-year-old Chilean international passed up the possible opportunity to move to the Premier League, choosing instead to make the temporary switch back to his home continent.
Gunners boss Arsene Wenger has been credited with an interest in bringing Vargas's former team-mate Edinson Cavani to the Emirates Stadium this month, but with the Uruguayan likely to cost in excess of £30million, a deal for the former Universidad de Chile star proved to be a more viable option.
However, Gremio have moved quickly to tie up Vargas, beating rivals Sao Paulo and Flamengo, completing a deal which allows Napoli to recall the player at any point during the year-long loan.
"It was a long negotiation, exhausting, but worth it for the quality that Vargas can add to our group," director of football Rui Costa told Lancenet.
Vargas will leave Italy later this evening and is expected to land in Porto Alegre around midday Saturday, where he will be presented to the media.