Arbitrator Tammy Brynie’s long-awaited decision means that hundreds of employees who originally applied for the positions when former commissioner John J. O’Brien was in charge will be offered an opportunity to apply again. It means that the successful candidates, who in most cases are still on the job, will have to reapply for their positions and could be removed.

“We’re overjoyed, “ said David J. Holway, president of the National ­Association of Government Employees, which sued the trial court to refill the positions. “Now we can get this ­behind us so the whole Trial Court can move forward.”

The union had filed grievances when the promotions were originally handed out, saying the losing candidates were at least as qualified as, and had more seniority than, the successful candidates. At the time, arbitrators rejected the union’s claims amid assurances from the Probation Department that the hiring process was fair.

But the union sued to reverse the decisions after the Globe and the Trial Court’s independent counsel, Paul F. Ware Jr., found in 2010 that O’Brien oversaw a rigged hiring process. Ware said that hiring and promotion decisions were “orchestrated from beginning to end in favor of connected candidates.”

Earlier this year, Suffolk Superior Court Judge Thomas Connolly sided with the union, ruling that the decisions were tainted by corruption. He sent the case back to an arbitrator to decide what action to take.

“Everybody understands in these instances the fix was in,” said Holway. “The arbitrator had no choice but to overturn those 10 appointments.”

The case represents the first ­successful effort to erase O’Brien’s legacy of political ­favoritism at the Probation Depart­ment, the agency that supervises criminals serving sentences in the community.

Earlier this year, O’Brien and two aides were indicted by a federal grand jury, charged with racketeering and fraud. O’Brien also faces state charges that he traded campaign donations to Timothy P. Cahill, former state treasurer, in exchange for a job at the state lottery for O’Brien’s wife, Laurie.

A spokeswoman for the Trial Court, which oversees probation, said the court will now “move forward with a reselection process and will ensure that it is totally based on merit.

“The Trial Court does not condone and will not defend any improprieties in hiring or promotion practices,” said the spokeswoman, Joan Kenney. “With this decision, we are still addressing well-documented ­issues of impropriety and injustice that occurred in the Probation Department, and we support the arbitrator’s decision.”

In her 79-page ruling, Brynie detailed the process by which top probation officials selected 11 employees for promotion.

She tried to determine whether they were the best choice, but was hampered by a lack of cooperation.

Not only did the Trial Court fail to participate in hearings, she wrote, but Francis Wall and Patricia Walsh, the two deputy commissioners who knew the most about O’Brien’s employment practices, refused to ­answer questions.

Even without all available information, Brynie found that in 10 of 11 cases, factors other than qualifications and experience played a role in the successful candidate’s selection.

Probation officer Jason Harder, who lost out on a job in 2005 to a less senior employee who was a family friend of a deputy commissioner, said the arbitrator’s decision was a step in the right direction.

Under the ruling, Harder and up to 70 other people who originally applied for the probation officer position at Hampshire Superior Court in Northampton will get a second chance at the post.

The candidate who originally won the Northampton job, Christopher Hoffman, was subsequently promoted and now faces charges that he threatened a witness in the FBI investigation of corruption within the Probation Department. Hoffman has been placed on administrative leave while his family friend and mentor, former deputy commissioner ­William Burke, was indicted on federal racketeering charges earlier this year.