"India has agreed to extradite Nur Hossain," Foreign Minister A H Mahmood Ali told Parliament while replying to a question by a lawmaker of the main opposition Jatiya Party.
He said India's assurance came after the request was made to Sushma Swaraj during her maiden stand-alone official tour here as the External Affairs Minister.
He said an official request will now be sent to India to bring back Hossain.
He had made the remarks when asked about Bangladesh's demand for Hossain's extradition.
Bangladesh's home ministry earlier said the government was "continuing efforts to bring Nur Hossain home".
The ministry said it expected Hossain's repatriation to be an easy process as the two countries last year inked an extradition treaty to exchange wanted criminals hiding on each other's soil.
Hossain is likely to be the first Bangladeshi to be deported from India since the signing of the extradition pact between the two countries in December 2013.
Hossain, a local leader of the ruling Awami League, is alleged to be the key mastermind behind the murders of seven people in suburban Narayanganj nearly three months ago.
The murders sparked a massive public outrage as it was alleged that several personnel of the elite anti-crime Rapid Action Battalion (RAB) were involved in the crime.
The seven people murdered, including a lawyer, were kidnapped by assailants from the suburban river port city on April 27 and their nearly decomposed bodies were retrieved later from the Shitalakya river.
The three officers - an army lieutenant colonel, a major and a navy lieutenant commander -- were arrested subsequently and after weeks of interrogation in police custody they confessed their involvement in pre-trial testimonies separately before a magistrate.