Mr Singh, who is 62, has begun a three-year term as president.
He met this morning with current president Nitin Gadkari and BJP veteran leader LK Advani, reportedly to seek their blessings.
Mr Gadkari till yesterday seemed headed to the finish line of an unprecedented second consecutive term, a prospect which Mr Advani had been fighting with other senior BJP leaders like Yashwant Sinha.
Their opposition to Mr Gadkari is based partly on the allegations of financial malpractice by the Purti Group, a vast business empire founded by Mr Gadkari in 2000. The company and its investor firms are being investigated for tax evasion and money laundering.
Yesterday, income tax officials began a new round of visits at different locations in Mumbai linked to the Purti Group. Mr Gadkari's detractors sensed a chance to scale up their campaign against him.
The RSS, which had said it would support only Mr Gadkari for president, now found it hard to stick by its man and agreed to back a consensus candidate selected by BJP leaders.
In the evening, Mr Gadkari and Mr Advani met in Mumbai with senior RSS leader Bhaiyyaji Joshi. Mr Advani had made it clear that he would support a bid by former Finance Minister Yashwant Sinha for president.
Mr Gadkari then offered to quit and proposed Mr Singh as president. Mr Advani was initially not convinced but came around. In Delhi, senior BJP leaders like Sushma Swaraj, Arun Jaitley and Venkaiah Naidu met and agreed on Mr Singh's suitability.
Mr Gadkari then issued a statement refuting the charges of graft against him; he said he would not seek re-election because he did not want to hurt his party in any way. (Read: Political conspiracy to tarnish my image, alleges Gadkari)
In his earlier term as president from 2006 to 2009, Mr Singh shared a fractious relationship with Gujarat chief minister Narendra Modi, who could be the BJP's prime ministerial candidate in the general elections next year. Today, Mr Modi tweeted- I called up Shri Rajnath Singh ji & congratulated him. He brings with him vast experience of both organisation & administration.