The $13.3 million will be used to renovate the former Baldwin House complex on West Washington Street.
University System of Maryland officials are waiting to see exactly how the money is to be spent, said spokesman Chris Hart.
"We're happy that the governor has seen fit to fund this project and we look forward to details on the numbers," he said.
The university has pegged the total cost, including design and equipment, at $15.3 million. About $800,000 already has been spent.
Glendening has used the campus as an example of his Smart Growth initiative in action, saying it will be a catalyst for revitalization elsewhere in downtown Hagerstown.
The $4.4 million open space idea was drafted by a group of Hagerstown businesspeople and endorsed by local elected officials.
"The community feels it is critical to the success of the university. It's clearly the county's top priority right now," said Washington County Commissioners President Gregory I. Snook.
Sen. Donald F. Munson, R-Washington, said he remains cautiously optimistic that the open space funding will be forthcoming.
"If there's one thing I got out of the governor's speech yesterday it was a commitment to the revitalization of downtowns. Frankly, this project in Hagerstown is timely, it's sound, it's a vital project to the revitalization of downtown," he said.
Munson said although he continues to have reservations about a lack of parking and room for expansion around the downtown campus, he views the university project as an opportunity.
"If someone wants to become a physicist, they shouldn't have to leave Washington County. My constituents need to have the advantage of those opportunities," he said.
Hagerstown and Washington County governments will have to be willing to support the project with police services, transportation and parking, he said.
Del. Sue Hecht, D-Frederick/Washington, said the university project must survive the legislature's budget cuts.
"We're going to have to fight to keep it in," said Hecht, who is on the House Appropriations Committee.
Glendening will release other details about his proposed capital budget on Tuesday. Local officials will be looking to see if it funds other Washington County projects, especially a national Civil War Museum.
Washington County's best chance of getting funding is through the governor's initial budget proposal, said Del. Robert A. McKee, R-Washington.
Competition is fierce for funding for projects added later this session in what is known as a supplemental budget.
Staff writer Scott Butki contributed to this story.