Rangers, 54 times Scottish champions, were demoted to the fourth division for financial irregularities in 2012 but are now in the second tier.
The caretaker manager's resignation comes amid a battle for control of the club and to raise cash to stay afloat.
"Kenny, who has been a fantastic servant of the club, will serve his 12-month notice period, during which time he will remain 100 percent committed to his normal duties," Rangers said in a statement.
"The club respects Kenny’s decision and he will continue to have the full support of everybody at Rangers."
McDowall, 51, took over in December from former Rangers striker Ally McCoist, who had been in charge of the fallen Scottish giants since 2011. He was previously assistant manager.
Rangers said earlier on Monday that it was in talks to agree new funding which could use the club's Ibrox stadium as security..
According to media reports, two stakeholders -- Sports Direct founder and Newcastle United owner Mike Ashley, and a wealthy consortium called the Three Bears -- are separately ready to provide 10 million pounds ($15 million) loans, with Ashley reported to want Ibrox as protection.
(Reporting by Alan Baldwin, editing by Peter Rutherford)
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