Bassel Khartabil's wife said he was killed in October 2015 after receiving a death sentence.
"Words are difficult to come by," she wrote. "Thank you for killing my lover."
The Wikipedia contributor and founder of Creative Commons Syria was first detained in March 2012.
After nine months of incommunicado detention, he was moved to Adra prison in Damascus, where his family were allowed to visit him.
But he was moved from the prison to an unknown destination in October 2015, and supporters had until now held out hope he might be alive.
Soon after his disappearance in 2015, his wife Noura Ghazi Safadi said she did not know if he was alive or dead.
But she said she had been contacted by self-declared Syrian government insiders who told her that he had been sentenced to death.
Bassel Khartabil, a Syrian-Palestinian, was named a Top Global Thinker by Foreign Policy magazine in 2012 and given the Digital Freedom Award by Index on Censorship in 2013.
In 2013, he was described by two European parliamentarians as being "credited with opening up the internet in Syria - a country with a notorious record of online censorship - and vastly extending online access and knowledge to the Syrian people".
Noura Ghazi Safadi described her husband as "unbelievably romantic" in a 2015 interview with the Electronic Intifada news website, adding that he "wasn't a typical internet geek".
"He used to give me a red rose every day since we became lovers until the day of his imprisonment," she said.
Khartabil, an open source web developer, had co-founded the #NewPalmyra project, which creates digitally reconstructions of the ancient Syrian city.
Wikipedia founder Jimmy Wales said on Twitter that he was "saddened and outraged in equal measure" to learn of the execution.
A Syrian internet freedom activist was executed soon after he disappeared from prison in late 2015, his wife and supporters say they have learned.