Giles led the Bears to the LV= County Championship title as well as the final of the Clydesdale Bank 40 in 2012, but stepped down from his position to take charge of England's limited-overs sides.
Brown, a former England and Scotland all-rounder in one-day internationals, has been Warwickshire's assistant coach for the last four years.
The 43-year-old beat off stiff competition to take the reins at Edgbaston and knows he has some big shoes to fill.
"It is a real honour for me to be given this opportunity to lead Warwickshire Cricket," he said.
"As a club and as a squad we are in a good place at the moment but we are very determined to deliver sustained success on the pitch.
"This will only be achieved if we keep working hard, stick together and perform consistently.
"Last year's success is now just that - as champions every other team will be looking to take our scalp so we need to be better prepared than ever."
Graeme Welch has been appointed assistant coach after being pipped to the top job by Brown, while Tony Frost will join Warwickshire's ranks as batting coach.
Chief executive Colin Povey added: "It will provide continuity after a successful 2012 in which we won the LV= County Championship title and ensure that the club's established cricket policies and processes remain in place.
"Dougie knows the club and the current crop of players as well as anyone, so he is well placed to take the squad forward."
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