It follows a review of the party’s structure in Derry, with Ms Anderson one of several members asked to quit their roles.
On Tuesday Ms Anderson said the party recommendation had come as a “body blow”.
Her political career has spanned several decades, both at Stormont and Brussels.
Ms Anderson published a video on Twitter on Tuesday evening confirming that she would not run in the next election.
She said she had received solidarity from supporters “across Derry and beyond” urging her to stay on in the role and described it as a difficult time for her and Karen Mullan, the party’s other MLA for Foyle.
“The national leadership correctly wants to re-energise our base and since coming back from Europe I have sought to do just that,” she said.
“Throughout my life as a republican I have always put our struggle first and so, in wanting what the leadership believe to be best for it, I have decided not to seek the nomination to contest the next assembly election.”
She added that she would support whoever the local membership selected as a candidate for the May 2022 election, to help build support in the constituency.Ms Anderson first joined the assembly in 2007, later becoming the party’s MEP in 2012.
She was co-opted again as MLA for Foyle in January 2020, having lost her seat in Brussels when the UK left the European Union (EU).
There is no word yet on whether the party’s other MLA, Karen Mullan, who was also co-opted into Foyle in 2017 to replace Elisha McCallion who took the Foyle Westminster seat, will also fall on her sword and step down.
McCallion resigned as a senator last year after it was revealed she received a £10,000 Coronavirus business grant a and failed to declare it.Tags: