McCoist, 52, has been in charge at Ibrox since 2011 and taken the 54-times Scottish champions back to the second tier following their demotion to the fourth division for financial irregularities in 2012.
In a statement to the Stock Exchange on Monday the club confirmed he had resigned but was working a 12-month notice with his salary increased to 750,000 pounds a year.
"The directors will hold discussions with Mr McCoist to seek an amicable solution in the best interests of the company, and expect to be in a position to make a further announcement before the end of the week," the statement read.
The decision ends the uncertainty surrounding the future of McCoist, the club's all-time record goalscorer, following reports on Friday that he had offered his resignation.
Rangers, who were officially founded in 1873, had never played outside the top division from the formation of the Scottish League in 1890 until they were demoted in 2012, a year after winning their 54th Scottish title.
Rangers are currently nine points behind leaders Hearts in the Championship (second tier) as they chase a third successive promotion and a return to the top flight.
(The story changes date of official founding in sixth par)
(Reporting by Mike Collett. Editing by Patrick Johnston)
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