He outlined his plan to give everyone in Scotland a say during a speech in Campbeltown, Argyll, where he held a cabinet meeting with his key ministerial team.
He said: "The process of drawing up a constitution in itself will energise and inspire people.
"It will provide us with a chance to reflect on the democracy and society we want to live in, the values that we most cherish.
"Independence offers the opportunity for Scotland to move away from that outdated and profoundly undemocratic Westminster system - one which for two-thirds of my life has delivered governments with no popular mandate in Scotland."
The UK is the only nation in the European Union or Commonwealth without a written constitution or Constitution Act, Mr Salmond said.
However, Scottish Liberal Democrat leader Willie Rennie said: "Whilst I share Alex's view that we need a written constitution to empower citizens, he overstates his case by branding the UK as profoundly undemocratic. The UK is not like North Korea nor China and he does his case no good by implying we are."
Scottish Conservative leader Ruth Davidson said: "As far as I can see, the only people who will be energised by the drawing up of a written constitution will be government lawyers and civil servants."