The 26-year-old has been expected to complete a permanent move away from Arsenal for some time now after falling out of favour under Mikel Arteta.
Torreira found it difficult to make his mark at Atletico Madrid in the 2020-21 season but shone for Fiorentina last season with five goals and two assists from 31 Serie A appearances.
La Viola were understood to possess an option to make Torreira's stay permanent for a £12.5m fee, but the Italian club tried to lower the asking price and could not agree a deal with Arsenal.
The Uruguay international therefore returned to London Colney and was a part of Arsenal's squad for their pre-season tour of the USA, but that did not signal the start of a revival in North London.
Despite Torreira's agent revealing that a pre-contract agreement was in place with Valencia, Galatasaray quickly jumped to the head of the queue for the ex-Sampdoria man.
However, Torreira was allegedly stalling over a move to the Turkish giants, as he wanted more time to come to a decision on his future after his switch to Fiorentina fell through.
Now, journalist Fabrizio Romano reports that Torreira has finally agreed to join Galatasaray, one year before his deal with Arsenal is due to expire.
Romano adds that the midfielder will soon jet off to Turkey to complete his medical and sign his contract, and Arsenal are set to receive a €7m (£5.9m) fee for his sale.
Torreira prepares to leave Arsenal after registering four goals and six assists in 89 games for the Gunners since 2018, and the North London club will take a significant hit on the £25.8m they shelled out to sign him.
The South American won the FA Cup and Community Shield during his time in North London, but he did not play in either final after recovering from a serious ankle injury.
Torreira's exit would leave Granit Xhaka, Thomas Partey, Albert Sambi Lokonga, Mohamed Elneny and Ainsley Maitland-Niles to fight it out for the midfield spots in Arsenal's XI, although Oleksandr Zinchenko can also deputise in the engine room.
Arteta's side are still being tipped to sign a new lynchpin before the transfer window closes, and the Spaniard has confirmed that his side are looking for more signings in the current window, which could see the Gunners ramp up their interest in Leicester City's Youri Tielemans.