Jagdev Lally was rushed to hospital after a passer-by found him collapsed off the High Street on April 14.
The 38-year-old, of no fixed address, had suffered significant head and facial injuries, which police say are consistent with being attacked and died on Friday.
Ashley Pace was previously charged with wounding and the 34-year-old, also of no fixed address, was remanded in custody to appear before Wolverhampton Crown Court on May 25.
This charge is now being reviewed.
Detective Inspector Jackie Nicholson said: "Mr Lally was sadly unable to survive his injuries and this is now a murder investigation.
"He was discovered near the Tollgate Shopping Centre at around 9am on April 14, and we're still keen to hear from anyone who was in and around the area earlier that morning and may have information which can help us."
The attack happened just over a week before two other violent incidents saw Karl Gallagher was stabbed to death in the town and a second man attacked with a machete at a petrol station.
Anyone with information can get in touch via Live Chat at west-midlands.police.uk, or via 101.
Alternatively, contact Crimestoppers anonymously on 0800 555 111.