Mr Brolly was in his early 80s.
He represented the East Derry constituency at Stormont from 2003 until his retirement in 2010.
The politician was an outspoken critic of abortion and in 2018 he resigned his membership of Sinn Féin in protest over the party’s policy on terminations.
Both Mr Brolly, his wife, Anne, a former Mayor of Limavady, and their son Proinnsias later joined the anti-abortion republican party, Aontú, which was formed just over a year ago.
Aontú’s deputy leader, Derry City Councillor Anne McCloskey, told BBC News NI she was “heartbroken” at news of her friend’s death.
She said Mr Brolly died unexpectedly at home in the middle of the night and his family were “devastated”.
Francie Brolly, who was a former teacher from Dungiven, was also a musician and songwriter who spoke Irish.
Ms McCloskey said he was at the “heart of the community” in Dungiven and would be sorely missed.
Sinn Féin vice president Michelle O’Neill also paid tribute to Mr Brolly in a statement on Thursday morning describing him as a “committed Irish republican”.
“Francie Brolly was a significant figure in the political life of east Derry for many years and will be missed by many,” she said.
“As a teacher, activist, campaigner and elected representative, he helped shape the community in his native Dungiven and further afield.
“Aside from politics, Francie also made a huge contribution to the musical and cultural world with his songs he recorded and performed alongside his wife, Anne and his love of the Irish language.”
Another son of the couple, Joe Brolly, is a barrister and a well-known gaelic games pundit.
Joe was a member of the All-Ireland winning Derry Gaelic Football team of 1993.
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