The executions were the first carried out for election-related incidents.
Iranian authorities arrested around 4,000 protesters including journalists and reformist politicians in a massive crackdown in the weeks after the disputed election.
The two were among 11 people sentenced to death on similar charges in the wake of post-election protests.
But Nasrin Sotoudeh, Rahmanipour's lawyer, denied that her client had any role in the post-election disruption.
"He was arrested in Farvardin [the Iranian month covering March-April] before the [presidential] election and charged with co-operation with the [monarchist] Kingdom Assembly," Sotoudeh told AFP.
She also said she was prevented from representing Rahmanipour at his "show trial" in July and that many of the charges were brought against him when he was a minor.
"He confessed because of threats against his family," she said, adding that she was shocked at the news of the executions since she and her client's family had still been waiting for word from the appeals court.
Baqer Moin, an Iranian author and journalist, said the execution was a "political decision", likely intended to "set an example and to frighten some of the people who may shout a slogans that are not of the liking of the authorities".
"We don't really know which group they belong to, one of them is a monarchist and the other one is the Mujahideen group, obviously the Mujahideen group is not very popular but little is known about the monarchist group," he told Al Jazeera.
"Their lawyers have said that these people were arrested much before the elections, I suppose that they have been used as an example specifically as we are approaching the anniversary of the revolution."
He said: "It is an attempt to make sure that the radicals within the opposition movements are not going to take the lead in the anniversary of the revolution."
The June 12 presidential election plunged Iran into its deepest internal crisis since the 1979 Islamic revolution and exposed widening political divisions.
The reformist opposition says the election was rigged to secure the re-election of Mahmoud Ahmadinejad, the president.
Denying fraud, Tehran portrayed the protests as a foreign-backed bid to undermine Iran's Islamic system of government.