Christopher Lewis, 24, was killed following the shooting in Reginald Street, Chapeltown, on Wednesday, West Yorkshire Police have now confirmed.
A force spokesman said Mr Lewis, from Leeds, died yesterday (Thursday) in hospital.
Officers have now arrested two men on suspicion of murder and a woman on suspicion of assisting an offender in connection with the offence.
They remain in custody for questioning, the spokesman added.
Police patrols in the area have also been stepped up to reassure the community.
Officers, including armed police attended the scene and the National Police Air Service helicopter was also drafted in, following the shooting at about 7.15pm on Wednesday.
Detective Superintendent Jim Dunkerley, of the Homicide and Major Enquiry Team, who is leading the investigation, said: “Our investigation into the firearms discharge remains ongoing.
“Christopher was deliberately targeted and we firmly believe there are people who know who is responsible or witnessed the incident as it happened in broad daylight in a busy area."
Anyone who has any information or witnessed anything suspicious in the area is urged to contact the police via 101 or information can also be passed to Crimestoppers anonymously on 0800 555 111.