The former prime minister said a new form of federal home rule is needed to unite the country and avoid years of "bitter division".
Mr Brown was speaking at the Festival Of Ideas in Kirkcaldy, Fife, against the backdrop of a constitutional stand-off between the UK and Scottish governments over the calling of a second independence referendum.
He has already pledged to join forces with Scottish Labour leader Kezia Dugdale to campaign for a People's Constitutional Convention to look at how power is distributed across the nations and regions of the UK.
Mr Brown, an architect of the 2014 "vow" promising Holyrood more powers in the event of a No vote to independence, proposed that a range of controls should be passed to the Scottish Parliament after Brexit.
These include the setting of VAT rates, the power to sign international treaties, and controls over agriculture, fisheries, environmental regulation, employment and energy.
The former PM also called for the repatriation to Scotland of £800 million of money now spent by the European Union, and propose the Bank of England becomes the Bank of England, Scotland, Wales and Northern Ireland with fully-staffed representation in Scotland "to reinforce the fact that the pound is for everyone".
Mr Brown 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.
"The patriotic way means that Scotland is not caught between a die-hard conservatism that denies the Scottish Parliament the powers it needs and a hard-line nationalism that throws away the resources we secure from being part of the Union.
"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 hard-line nationalism."
Additional reporting by Press Association.