The deaths were recorded at the University Hospitals Birmingham NHS Foundation Trust earlier this week.
One person died on Wednesday and another died a day later at the trust, which runs the Queen Elizabeth Hospital.
It means the total number of coronavirus deaths in hospitals across the Black Country, Birmingham and Staffordshire stands at 2,573.
In England, the death toll in hospitals increased by 16 to 29,735. The UK-wide figure has not yet been released.
A spokesman for NHS England said: "A further 16 people, who tested positive for the coronavirus (Covid-19) have died, bringing the total number of confirmed reported deaths in hospitals in England to 29,735.
"Patients were aged between 69 and 97 years old. All had known underlying health conditions."
A further 700 people have died in care homes across the Black Country, Birmingham and Staffordshire, according to the latest Office for National Statistics data.
A total of 982 patients have died at the University Hospitals Birmingham NHS Foundation Trust.
At the Royal Wolverhampton NHS Trust, which runs New Cross and Cannock Chase hospitals, a total of 288 Covid-19 patients have died so far, and 230 people have died at Walsall Healthcare NHS Trust which runs Walsall Manor.
A total of 264 Covid-19 patients have died at Russells Hall Hospital, run by the Dudley Group NHS Foundation Trust, and 383 people have died at the Sandwell and West Birmingham NHS Trust, which runs Sandwell General and City hospitals.
In Staffordshire, 355 people have died at the University Hospitals of North Midlands NHS Trust which runs the major hospitals in Stafford and Stoke.