The accused were identified as Dolly Choudhary, 21, and her fiancé Manish Choudhary, 28, they said.
A case was registered on August 16 on the basis of a complaint from the victim's father, according to the police.
The family of Sushil Kumar told the police that he had a relationship with the woman for the last six seven years and about a year and a half ago she began to live with a person named Mohit Mavi in Greater Noida, Randeep Singh Randhawa, deputy police commissioner (middle) said.
On Friday, the police visited the woman's house and questioned her about the whereabouts of Kumar. Initially, the woman tried to deceive the police, but in case of persistent interrogation she admitted that she had committed the crime, the officer said.
Dolly told police that she had gone to Greater Noida about two years ago for a job where she met Mohit Mavi, a contractor who provided manpower to a company. Mavi offered her a job for Rs 10,000. She eventually went to live with Mavi and shared an intimate relationship, the officer added.
Furious about the fact that Mavi would marry Dolly, Kumar started to blackmail her and threaten her with her nude photos. Sure of his constant threats, Dolly came up with a plan to eliminate him with the help of her fiancé Manish Chaudhary, the DCP said.
On August 11, at Dolly's insistence, her fiancé arranged a room in a hotel in Mathura. The same evening Kumar reached Mathura and contacted Dolly. She went to meet him near the train station. After visiting a few places, Kumar brought her to a hotel room where he ordered food and cold drinks. While he was in the laundry room, Dolly mixed sleeping pills in his drink. He becomes unconscious after he has consumed it.
Then she called her fiancé Choudhary in the hotel and later threw his body into a river at the old Yamuna bridge in Mathura's Laxmi Nagar.