But construction of smaller facilities in all eight wards to replace the shelter won't be finished, meaning the city would need to expand its use of motels to house homeless families if there are not enough landlords willing to rent to residents with temporary vouchers. The letter to residents promised "access to appropriate shelter" to anyone who hasn't found housing by the end of the year.
Barring new snags, the closure of D.C. General would bring an end to an institution made notorious after the disappearance of 8-year-old Relisha Rudd in 2014. And it comes as Bowser, running for a second term this year, vows to make good on a promise key to her administration's focus on ending homelessness and increasing affordable housing.
"We are starting to realize our plan to make sure that we have safe and dignified housing for when a family has an emergency," Bowser said in an interview Sunday. "Some of the steps have been rocky getting to this point, but we are delivering on a plan we ought to be proud of."
Those steps include revelations that campaign donors to the mayor stood to gain from her administration's choices for replacement facilities, the D.C. Council swapping out some of those sites, and fights waged by citizen groups.
At one point, Bowser called D.C. Council Chairman Phil Mendelson a vulgarity for suggesting that D.C. General could close by 2018 without her administration's original plan.
Now she says closure is in sight by year's end.
A women's shelter in Ward 2 opened last year, and Bowser's administration says facilities for homeless families are scheduled to open this fall in Ward 4 in Northwest Washington and east of the Anacostia River in Wards 7 and 8. The rest are set to open next year, except for a shelter in Ward 1 that is in the design phase.
The problem of housing homeless families in the nation's capital goes beyond D.C. General.
Hundreds more are placed in temporary shelters in motels, mostly along New York Avenue in Northeast. The number of homeless adults and children in families dipped last year, although their ranks are still higher than five years ago.
Shelters and housing vouchers are supposed to be temporary measures while adults become self-sufficient, but the lack of affordable housing and the declining stock of large apartments make it harder for families to pay their own way.
"People want us to do more, and I want to provide more services and focus more on how we can have affordable housing at the end of the line, so once people have the services they need from (the Department of Human Services), there is safe and affordable housing for them," Bowser said.
City officials will stop placing homeless families at D.C. General in May. In the coming weeks, a vacant building set for demolition will be fenced off and eventually the complexes where families live will come down.
"We want to make sure this building is not used for shelter ever again," said Kristy Greenwalt, director of the D.C. Interagency Council on Homelessness. "When shelters are set to close and there isn't strong communication, people who are staying at those facilities naturally get very nervous."
At a Sunday evening meeting to discuss the D.C. General closure, shelter residents peppered city officials with questions about how they could afford to live in the District and find landlords willing to rent to them.
"Are you pushing us out?" one woman asked.
"No ma'am, we are not abandoning you," replied Jerrianne Anthony, a city official who reiterated that those who can't find housing would still have a roof over their head.
"Like a hotel?" another piped in.
"Another shelter," a woman sighed.
"You won't be out on the streets," Anthony said. "You'll have someplace to go."
For some residents, the closure of D.C. General couldn't come fast enough, even if it was better than the streets.
"It's an old D.C. General Hospital. They closed it down for a reason, and yet they have people here," said LaTonya Merrit, 45, who has lived in the shelter for seven months with two children. "Sometimes there's no hot water. We don't have a real cafeteria for us to eat. You have rats and mice running through the building."
Other residents said they were skeptical that smaller shelters would be any better than a megashelter.
"It won't be any different," said Jewel Johnson, a 27-year-old who recently arrived at D.C. General with two of her children after sleeping in cars and crashing at friends' places. "I just want somewhere safe that's mine."