Tividale ward councillor Sandra Hevican had been in a coma and on a ventilator at Walsall Manor Hospital.
The 55-year-old from Wednesbury passed away at 7.22am on Monday five weeks after testing positive, her family said.
She had been in hospital for four weeks after initially experiencing no symptoms apart from a headache.
Sandwell Council's interim leader, Councillor Maria Crompton, paid tribute to her as a "lovely lady" and "hardworking" councillor.
She said: "I have lost a very good friend and a dear colleague and I cannot imagine how awful it must be for her family.
"She was such a lovely, lovely lady. There was no side to her, she was just straight.
"She said exactly what she thought. She was really helpful and a hardworking person and I loved her to bits.
"It is just totally devastating. She was a lovely lady and it is heartbreaking, totally heartbreaking."
Councillor Hevican tested positive for coronavirus on February 13 after suffering a headache but having none of the typical coronavirus symptoms.
She was taken to hospital a week later, eventually being put into intensive care.
Her husband Robert, 58, explained last week: "On the day the test came back, she was feeling fine. But on her last day of self-isolation, which was February 20, I had to call paramedics because her breathing was not too good.
"She has been in hospital since then. Unfortunately her condition did not improve and she had to go into intensive care.
"She had a collapsed lung on March 12 and it has been an absolute nightmare since then.
"It has been absolutely dreadful. It has been touch and go for the last week."
Mr Hevican was warned by doctors that it was unlikely his wife of 35 years would recover.
He added: "The thing is the headache. Headaches aren't something you should be tested for but that is what we had.
"I must stress, that symptom is the only symptom we had. We did not have a high temperature, a loss of smell or cough.
"I never thought my future would not have my wife in it."
Alongside being a Sandwell councillor, a role which she served for seven years, she was also a housing benefits officer at Wolverhampton Council.
Councillor Hevican was highly thought of at Sandwell Council and Wolverhampton Council, Tipton Green councillor Ian Jones said.
Alison Shannon, Wolverhampton Council's chief accountant, said: "Sandra was a highly experienced and valued member of the revenues and benefits team, she came to work for us in 2000 after moving over from Sandwell Council.
"We will remember her for her total commitment to her role as well as her kindness, her plain speaking, her sense of fun and for being a big Albion fan.
"Our condolences and thoughts go out to Sandra’s husband Rob and son Greg, family, friends and colleagues at this sad time."
Tim Johnson, Wolverhampton Council's chief executive, said: "I was deeply saddened to hear that Sandra had passed away and my thoughts are with her family, as well as her many friends and colleagues here at the council.
"To lose a member of our work family to this terrible disease gives tomorrow's National Day of Reflection an extra poignancy and she will be very much at the forefront of our thoughts."
Fellow Tividale ward councillor Lorraine Ashman added: "Sandra was not only a work colleague and working councillor, she was a really good friend, who was highly thought of by us.
"She was reliable, thoughtful and extremely kind. She will be greatly missed, it is a shock to everyone."
Councillor Hevican was first elected in May 2014 and served the Tividale ward.
Her most recent positions within Sandwell Council were vice-chair of the planning committee, member of the ethical standards and member development committee and member of the audit and risk assurance committee.
Councillor Hevican has sat on other various committees and panels during her term of office including the safer neighbourhoods and active communities scrutiny board, the housing, jobs and economy scrutiny board, the Rowley Regis town improvement board and the children’s services and education scrutiny board.