The club has said he will serve a 12-month notice period under the terms of his contract, as his predecessor Ally McCoist intended to.
A statement from Ibrox said the 51-year-old will "remain 100% committed to his normal duties".
Rangers say McDowall made the decision to resign for "personal reasons".
He stepped up from his assistant's role when McCoist was placed on gardening leave last month.
His reign opened with a 4-0 defeat away to Hibernian, with wins against Dumbarton and Alloa Athletic following before Friday's abandoned game against runaway Championship leaders Hearts.
Rangers trail the Edinburgh side by 13 points.
"The club respects Kenny's decision and he will continue to have the full support of everybody at Rangers," added the statement.
McCoist, who had been in charge since the summer of 2011, was removed from his duties only nine days into his 12-month notice but remains on the pay roll.
Former St Mirren striker McDowall joined Rangers as first-team coach under Walter Smith in 2007, helping the club win three top flight titles in a row from 2008-09 to 2010-11, and was promoted to the assistant's position when McCoist became manager.
He had previously been working as a youth coach with Glasgow rivals Celtic.
Kenny McDowall took Rangers' first-team for training as normal on Tuesday despite having tendered his resignation as caretaker manager the day before.