Marie Penman was elected to Fife Council after winning the first local by-election in Scotland this year.
She said it was a “huge privilege” to be voted in as the new councillor for Kirkcaldy East, which is part of Mr Brown’s Westminster constituency of Kirkcaldy and Cowdenbeath.
The former prime minister, who played a pivotal role in the campaign to keep Scotland in the UK, has since announced he is stepping down from the House of Commons at May’s General Election.
Labour will be fighting hard to retain his seat, as the number of Scottish MPs it secures will be crucial to Ed Miliband’s chances of getting in to Downing Street.
But with the nationalists ahead of Labour in Scottish polls, Douglas Chapman, the SNP’s convener responsible for organisation, said: “This SNP victory in Gordon Brown’s backyard will chill Labour to the core across Scotland and shows how little trust people have left in the Labour Party.”
Mr Chapman, who is also an SNP councillor for Rosyth and North Queensferry, added: “Marie will be a strong advocate for the people of Kirkcaldy East, and is another strong woman who has won for the SNP. She will be a fantastic addition to the SNP council team in Fife.”
The by-election result was an SNP hold as the party had won one of the ward’s three seats in the 2012 main Fife election, but there was a swing of 12.8 per cent from Labour to the nationalists.
Ms Penman secured 1,460 of the first preference votes, ahead of 1,088 for Labour.