Eighty-two years and eight months after they were arrested and framed for raping two white women on board a freight train heading to Memphis, justice has finally been served for all of the Scottsboro Nine, though none are alive to enjoy the bittersweet moment.

Alabama’s parole board granted posthumous pardons on Thursday for the three remaining members of the group who had yet to have their convictions rescinded – finally laying to rest one of the great miscarriages of the civil rights era. The pardons were issued for Haywood Patterson, Charlie Weems and Andy Wright, all of whom were initially sentenced to death and who served long prison sentences having been found guilty by all-white juries on trumped-up charges.

The nine deceased African Americans were represented at the parole board meeting, in the absence of any family members, by Sheila Washington, a Scottsboro resident who has led the campaign to pardon the men. The last of the group, Clarence Norris, died in 1989.

Washington told the Guardian that holding the three pardon certificates in her hand had been “joyous and sad at the same time. I feel like jumping up and down and rejoicing for them, because this is something they wanted in their lifetimes but it never happened.”

The certificates will next month be placed in pride of place at the Scottsboro Boys Museum and Cultural Center that Washington founded in a disused church near the centre of town. “Although they won’t be here to see it, the story of the nine will now be told – that all of them have finally been declared innocent.”

The nine boys entered into an altercation with some white youths as they were on the freight train passing through Alabama, on the night of 25 March 1931. When the train stopped at Scottsboro a posse of local white men boarded the train and took the teenagers captive; they also found two white women on board, who said they had been raped.

Although one of the women recanted her story in court, the nine were still sentenced to death by all-white juries. The case was to have enduring legal ramifications – the US supreme court ruled on the back of it that black people could not be excluded from juries on racial grounds.

Five of the accused teenagers – Olen Montgomery, Ozie Powell, Willie Roberson, Eugene Williams and Roy Wright – had their convictions overturned on appeal. In 1976, Norris became the only Scottsboro Boy to be pardoned while alive. That left three with convictions still on the books – until Thursday morning.

To clear the way for the pardons, the Alabama legislature had to introduce a new law allowing posthumous pardons, honed specifically to this case. Arthur Orr, a Republican state senator who sponsored the rule change, told the parole board: “Today is a reminder that it is never too late to right a wrong. We cannot go back in time and change the course of history, but we can change how we respond.”

Alabama’s governor, Robert Bentley, said in a statement that the pardons had been “long overdue. The Scottsboro Boys have finally received justice.”

Washington said she hoped that the resolution of this case would spill over to other states and inspire them to consider pardons in similarly grievous miscarriages of justice. She said she had already been contacted by one of the group known as the Central Park Five, asking for advice on how to seek redress.

The five men in that notorious case had their convictions, for the brutal 1989 rape of a jogger in New York, vacated 11 years ago, after DNA evidence proved the guilt of another man. They have not, however, been exonerated.