The 27-year-old has been heavily linked with a move throughout the summer and was previously expected to join Spartak Moscow, but that failed to materialise.
The transfer window has closed for most European leagues, but Turkish clubs are afforded at least another week to conclude their summer business.
Gala have used that to their advantage to secure a permanent deal for Sanchez, who will be eager to transition to the Turkish top flight with his Spurs career hanging by a thread.
Romano reports that the Super Lig giants have sanctioned a deal worth around an initial €10 million, but the total agreement could potentially rise to €15m due to performance-related add-ons.
Sanchez has agreed to pledge the next four years of his career to Gala, which will keep him associated with the club until 2027.
The Colombia international is expected to undergo medical examinations in his homeland before landing at Rams Park to sign on the dotted line.
Sanchez has only managed 76 minutes of Premier League football this season and will welcome the chance to reignite his career with the Super Lig title holders.
He played 90 minutes in the Carabao Cup second-round clash against Fulham but missed his spot kick in the penalty shoot-out, resulting in an early elimination for Spurs.
Sanchez is set to be the third player to swap the Premier League for Gala this summer, following in the footsteps of Wilfried Zaha and Hakim Ziyech.
He will join Tottenham teammate Tanguy Ndombele at Gala, with the Frenchman expected to travel to Istanbul later today to complete his move, having completed parts of his medical.
Ndombele will join Gala on a season-long loan, which features a purchase option that can be activated by the Turkish outfit at the end of the season.
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