Deputy President Cyril Ramaphosa should naturally become African National Congress (ANC) leader when.
Mngqithi replaces Muhsin Ertugral who stepped down from the position on Monday.
"Lamontville Golden Arrows welcome back Manqoba Mngqithi who was an important part of the growth of the Arrows team both as regards with the identification of young talent and the development of the Arrows style," the club said on their website.
"It is fantastic to have him back with us and we are certain the club can expect an immediate, and positive, change not only in the way we play but the results achieved."
Mngqithi, a former Arrows and AmaZulu mentor who helped Chippa United gain Premiership status this season, was fired by the newcomers in August just two games into the league campaign.
Ertugral said on Monday he hoped the side would recover from a run of poor form, handing in his resignation one year after taking the post.
Arrows were lying 13th in the league table ahead of this weekend's eighth round of matches, and were eliminated in the first round of the Telkom Knockout last week after a 3-1 defeat to Free State Stars in Bethlehem.
"It is always difficult to make decisions such as these but I honestly believe I am acting in the best interests of everyone here," Ertugral said.
"I know that there is appreciation for the fact that I have put the interests of the club first.
"The current situation is not through lack of trying or anything like that.
"When results are not forthcoming it becomes a situation which one needs to be realistic about, and make decisions which are for the good of the entire club."
Ertugal said he believed the side could achieve more under new management.
"Sometimes a change can have a positive effect and change the fortunes of a club," he said.
"This is a club which has great potential and I believe it is only a question of time before things improve.
"I have enjoyed my time here and worked well with the management and the players."