50-year-old Shah takes over from Singh who was appointed party president after the exit of Nitin Gadkari in controversial circumstances.
"I took over as the BJP President with a heavy heart. I felt helpless because of baseless allegations levelled against Nitin Gadkari. Since the Prime Minister has given me the responsibility of the Home Ministry...
"I convened the meeting of the Central Parliamentary Board and tendered resignation (as party chief)...The Parliamentary Board unanimously decided to appoint Amit Shah as the President of BJP," Singh said.
Singh had recently announced that he will relinquish his BJP role in keeping with the party's "one-man, one-post" principle.
"Shah is full of imaginative ideas and is good at organizational skills. As in charge of UP during lok Sabha polls, he got a roaring success. BJP had never been so successful in its history in UP," Singh said.
He also credited former Prime Minister Atal Bihari Vajpayee and Advani for making the Indian polity from unipolar to bipolar.
Singh said under Modi's leadership, the party got thumping majority in the lok Sabha elections, thus becoming the single largest party to get majority on its own after nearly 30 years.
BJP is set for major organisational changes following its victory in the 2014 lok Sabha polls as many of its senior leaders have become part of the Modi government.
The party's reorganisation will come ahead of Assembly elections in states like Maharashtra, Haryana, Jammu and Kashmir and Jharkhand later this year and early next year.
The RSS, BJP's ideological fountainhead, is also keen that the party should not be weakened after government formation.
It had already deputed two of its key leaders -- Ram Madhav and Shiv Prakash -- to work for BJP and new roles for both of them will be assigned by the new party chief. The two are likely to get key roles in the revamped party set-up with Madhav likely to be the new party general secretary.
The announcement of Shah's name as BJP President came after RSS' nod for the same.