Adams, who became leader of Sinn Fein in 1983 when it was the IRA's political wing, was for many years the best-known face of the movement seeking to end UK rule in Northern Ireland.
He later reinvented himself as a peacemaker after helping secure the 1998 Good Friday Agreement, which largely ended three decades of sectarian conflict known as the Troubles, in which about 3600 people were killed.
But Adams had long faced accusations that he was a member of the Provisional IRA, including from former members of the paramilitary group, which he has always denied.
Adams told the High Court this week that he was "never involved" in the IRA although he added that he believed that "people have the right to resist occupation".
"I'm glad that there is a peace process but I don't distance myself from the IRA," the 77-year-old said from the witness box on Tuesday, which was also St Patrick's Day.
The three claimants who were injured in three IRA bombings in the 1970s and 1990s were seeking a finding on the balance of probabilities that Adams was personally liable for the bombings as a senior member of the IRA.
But, after a civil trial at which Adams gave evidence over two days, the claimants' lawyer Anne Studd said on Friday - the last day of the two-week trial - that "the proceedings will be discontinued".
She said the claim would be dropped after "proceedings developed overnight".
Studd said the development was related to an argument around "abuse of process" but was then stopped by the judge who said: "Whatever statement your clients may wish to make outside court is entirely a matter for them."
"I am happy to make an order in the terms the parties have agreed," he continued.
Studd then said: "The claimants' view is that these proceedings have been affected by unfairness."
The end of the case means the High Court will not give a ruling on whether Adams was liable for the bombings or was a member of the IRA.
Adams, 77, who gave evidence in the trial but who was not in court on Friday, released a statement soon after the case was dropped, welcoming the decision by the claimants
"I attended the civil case out of respect for them," he said in a statement.
"This decision brings to an emphatic end, a case that should never have been brought."
with AP and PA
