Singh, a five-time MLA from Sidhi assembly seat, had been a strong contender for the post of CLP Leader along with the party''s Deputy Leader in the state assembly Rakesh Chaudhury.
A four-time MLA, Choudhury was appointed as the acting CLP Leader in Madhya Pradesh in November last year after the death of Jamuna Devi, 81, at an Indore hospital on September 24.
Singh''s appointment comes just days after Union Minister Kantilal Bhuria was named PCC chief for the state replacing Suresh Pachauri.
Since Bhuria belongs to the tribal community, the CLP leader had to be either from the Thakur or Brahmin community and hence names of both Singh and Chaudhary were doing the rounds for the post.
The Congress is hoping that appointment of Bhuria and Singh will revive the faction-ridden organisation in the state, which is under BJP rule for nearly eight years.
While Bhuria is a close associate of AICC general secretary and former Madhya Pradesh Chief Minister Digvijay Singh, Ajay Singh had also served as a minister in his government.
A senior leader in the party said that the Congress would "honour" the legacy of Arjun Singh.
The veteran Congress leader and former Union Minister, who had served in various capacities including as Madhya Pradesh Chief Minister, died last month.