German Rosler was appointed as Wigan Athletic manager at the weekend after the Championship club parted company with Owen Coyle last week.
Warburton has spent just over two years as sporting director at Griffin Park and has now been charged with the task of taking over first-team affairs, until the end of the season at least, by Brentford owner Matthew Benham.
Brentford chairman Cliff Brown told the club's official website: "Matthew was very clear about what he wanted.
"We have done very well this season with a squad Mark has helped to assemble and with the existing coaching and backroom staff.
"We believe Mark will offer continuity at a key time and enable us to build on the past two and a half years.
"Mark's coaching credentials are without question, he is highly qualified to deal with both professionals and our young players.
"Mark has a commitment to blooding young players in to the First Team and to the Academy and that remains important for the Club's development.
"Mark has done an exceptional job as Sporting Director since taking that role 30 months ago and we are happy he can step in to this new role seamlessly.
"We believe it will help the players and staff to work with someone they know and respect and we look forward to continuing success for Brentford Football Club."
The London club are fourth in the third tier of English football and Warburton's first game in charge will be Saturday's home clash with Oldham Athletic.
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