Singh got 238 votes against Ansari, the UPA nominee who was re-elected as Vice-President with 490 votes.
Singh thanked NDA and in particular the BJP leadership, for fielding him as a candidate.
"He gave a special thanks to Sushma Swaraj, Leader of the Opposition in Lok Sabha, for meticulously planning his campaign," Rudy said.
Singh claimed he had got more votes than the in-house calculations made by his election team.
"His campaign has also resulted in re-consolidation of NDA and over and joining of hands of AIADMK as a non-NDA, non-Congress party can be attributed to him," a party leader said.
Asked about this, Rudy said "Singh had a special word of appreciation for AIADMK supremo Jayalalithaa whom he had met on Monday in Chennai and who extended her party's unconditional support to him."
On behalf of BJP, party deputy Leader in Rajya Sabha Ravi Shankar Prasad extended warm greetings and congratulations to Ansari.