Singh will be replacing Nand Kumar Singh Chauhan, who stepped down from the post yesterday.
Chauhan's wish to work for his constituency, Khandwa, led him to make the decision.
"I have served as a Madhya Pradesh BJP party chief for the past four years and now I want to work for my constituency. I could not visit my constituency for the past four years. I spoke to the Chief Minister and urged him to relieve me from the party post," Chauhan told reporters, after the party's core committee meeting.
In the 2014 general elections, Chauhan was re-elected to the 16th Lok Sabha for a fifth term.
In another development, BJP Rajasthan president Ashok Parnami resigned from his position earlier today, citing personal reasons. (ANI)