Sakoun Khanthanoua reads a Maryland Health Connection pamphlet. The state’s online sign-up system has been plagued by technical issues. (Andrew Harrer/Bloomberg)

The board of Maryland’s health-insurance exchange voted Tuesday to hire Deloitte Consulting to replace most of the state’s troubled online marketplace with technology that has successfully worked in Connecticut.

The change is expected to cost between $40 million and $50 million to implement, plus some hardware and software costs, according to Isabel FitzGerald, Maryland’s secretary of information technology. Fitzgerald told board members that Maryland would adopt Connecticut’s system, which has run as smoothly as any in the country, largely as is, with little retrofitting.

It was not immediately clear whether there are any funds left from building the flawed Maryland system that could be used to cover some costs of the replacement.

Maryland was the one of the first states in the country to announce that it would launch its own online health-insurance marketplace under the 2010 Affordable Care Act. Now, the state is on track to be the first in the country to make a second attempt at building a system.

Maryland has spent more than $125.5 million to build and operate its exchange, which crashed within minutes of opening. While some components of the old system will likely be incorporated into the replacement, much of the work will need to be redone.

The total amount that Maryland is expected to spend on the two systems will be in the same range as what some other states have spent, FitzGerald told the board.

The federal government covers the cost of the computer code that the state needs to run its system, but Maryland would need to pay for implementation, software and hardware. The state, FitzGerald said, should be able to reuse a number of the hardware and software components from its current system.

Adopting Connecticut’s system would enable Maryland to get “core” functions in place in seven months, FitzGerald said. If that prediction holds up, Maryland would have an improved system by Nov. 15, the beginning of the next open enrollment period. The first enrollment period, for insurance this year, ended Monday.

The Maryland exchange’s shortcomings have embarrassed Maryland Gov. Martin O’Malley (D), who has portrayed himself as a results-oriented manager as he prepares for a possible 2016 White House bid. It is also a political liability for his preferred successor, Lt. Gov. Anthony G. Brown (D), who is running for governor and faces two major Democratic challengers in the June primary.

O’Malley and Brown issued a statement after the vote Tuesday that emphasized the parts of the health exchange that have worked well. They said hiring Deloitte would ensure that the online functions also were up to par.

“Maryland’s health exchange website did not meet expectations — a source of great frustration, especially for those who were trying to obtain healthcare for the very first time,” the statement said. “The vendors we hired failed to build us the platform they promised. So now that the first open enrollment period has ended, we’ve decided to upgrade our website.”

Maryland officials were warned for more than a year of grave and growing problems with the design and functionality of the system, according to a Washington Post investigation. Since the system’s failed launch, the state has been attempting to fix the system, hiring a series of consultants and firing the original contractor.

Brown has said that he was not given any day-to-day responsibilities in managing the exchange and was caught off guard by the extent of the Web site’s problems. On Tuesday, Brown was highly critical of the contractors hired by the state, saying “we fired the vendors who couldn’t get the job done.”

Brown’s gubernatorial rivals have seized on the exchange’s failures, although a Washington Post poll in mid-February found little evidence that the lieutenant governor has been damaged by the fallout. Residents of overwhelmingly Democratic Maryland, where Obama remains popular, are likely to be more forgiving of problems with the health exchange than voters elsewhere, analysts suggest.

Attorney General Douglas F. Gansler (D) said Tuesday night that Maryland’s decision to abandon its system was “the direct result of Lt. Governor Anthony Brown’s failure to fight for the Affordable Care Act. He put spin and posturing ahead of hard work and health care, and the proof is in the pudding.”

Republican candidates have also been taking swipes at Brown on the issue. One contender, real estate broker Larry Hogan, proposed this week that Brown be banned from further work on health care.

O’Malley has gone to great lengths in recent days to focus on the enrollments that the exchange has processed. More than 295,000 Marylanders have gained coverage by enrolling in Medicaid or in a private plan using the exchange, beating an overall goal of 260,000.

The Medicaid enrollment has exceeded expectations, while private enrollments have struggled. During the first open enrollment period, at least 63,000 people signed up for private health insurance, according to state officials, with hundreds — if not thousands — more expected to finish their enrollment in coming weeks.

That’s far short of the state’s original goal to enroll at least 150,000 people in private plans and less than a revised projection of 75,000 to 100,000 enrollees.

As of Monday, thousands of applications remained stuck in the system, and the Web site was struggling to handle increased traffic.

The decision to adopt Connecticut’s technology and hire Deloitte was made with limited, if any, input from a legislative oversight panel formed this year to explore what went wrong with the first exchange and what would work best in the future.

Sen. Thomas M. Middleton (D-Charles), one of the co-chairmen, said that he largely learned about the decision from media reports. Rep. Peter A. Hammen (D-Baltimore), the other co-chairman, said he had expected to be more involved and that “regular updates would have been helpful.”

“At the end of the day,” Hammen said, “we need a fully functioning exchange by the 15th of November.”

Mary Pat Flaherty contributed to this report.