The police got the leads to Mumbai after going through the mobile phones of the relatives and the call detail records (CDR) of the suspect. The shooter had taken a train to Mumbai soon after perpetrating the murder.
The police team will escort the arrested shooter to Lucknow from Mumbai on Thursday.
Bachchan, the leader of the right-wing Hindu outfit was shot dead on Sunday while he was out on a morning walk, barely a couple of kilometres away from the high-security Uttar Pradesh legislature complex in the heart of the state capital.
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Saffron-clad Ranjeet Bachchan, 40, who had founded the Vishwa Hindu Mahasabha, was shot in the head and his cousin Aditya Srivastava injured in the attack by an unidentified assailant who also snatched their mobile phones, according to Joint Commissioner of Police Naveen Arora.
The attacker had covered himself in a shawl and was on foot, police said quoting eyewitnesses.
Four police personnel, including a sub-inspector, were suspended for alleged laxity and a case has been registered at Hazratganj police station here in connection with the incident which occurred near the Collectorate building, days after Lucknow came under the police commissioner system with an aim to improve law and order.
Later, police released CCTV footage showing a suspect and announced a cash reward of Rs 50,000 for providing information, a senior official said.
The incident comes nearly four months after the leader of a little known Hindu Samaj Party was killed in the city.
On October 18, Kamlesh Tiwari (45), who was earlier associated with a faction of the Hindu Mahasabha, was found murdered at his home in the congested Naka Hindola area of the city.
(additional inputs from PTI)