Welch's inauguration ceremony, which had been scheduled for Thursday on the steps of City Hall, will instead be a virtual event.
Welch said he will remain in isolation for at least the next five days and will be sworn-in virtually from home on Thursday, Jan. 6, where he will also give a short speech.
"Let this serve as a reminder to all of us to get vaccinated and follow CDC guidelines to minimize the spread of COVID-19," Welch said in a statement. "While this is disappointing, I am incredibly thankful that my current symptoms are not serious, and I keep in my thoughts and prayers all the families who have lost so much more to this pandemic."
He said he has been vaccinated and got a booster in November. Welch first tested positive Monday morning using an at-home rapid test, the results of which were confirmed by a second PCR test later in the day.