Speaking at the Fife Festival Of Ideas, Brown set out his vision for a “patriotic Scottish way” to break with the past and secure more powers.
He said: “The third option, a patriotic Scottish way and free from the absolutism of the SNP and the do-nothing-ism of the Tories, is now essential because post-Brexit realities make the status quo redundant and require us to break with the past.
“The status quo has been overtaken by events because unless powers now with the European Union are repatriated from Brussels to the Scottish Parliament, the Welsh Assembly and the regions, Whitewall will have perpetrated one of the biggest power grabs by further centralising power.
“Tory and nationalist extremism should not rob us of a third option that can give the Scottish people more powers, offer honest answers about how we can pay for our public services and, faced with the post-Brexit threat to our employment and industry, address the urgent issue of how we create new jobs by exporting and trading successfully with Europe and the rest of the world.
“Most of all, a new third option can unify our country and end the bitter and divisive Yes v No conflict that will continue to rip us apart.
“It is time to transcend the bitter division and extremism of an inflexible, die-hard conservatism at war with an intransigent and even more hardline nationalism.”
The Independent reported that Brown’s idea of a new form of federal home rule would aim to unite the UK and avoid a bitter fight for independence.
He has previously pledged to join Scottish Labour leader Kezia Dougdale in exploring an alternative to full independence.
Scottish First Minister Nicola Sturgeon said on Saturday that Prime Minister Theresa May’s refusal to consider a second Scottish independence referendum would “shatter” the UK.