Mr Cardownie, who was also leader of the SNP group on the city council and deputy council leader. said voting Alba on the regional list would ensure more pro-independence MSPs were elected to Holyrood.
His move comes after iconic Edinburgh duo The Proclaimers announced at the weekend they would also be backing Alba.
The party is only fielding candidates on the list, urging independence supporters to vote SNP in the constituencies but Alba on the list to avoid “wasted” votes. The SNP wins so many constituency seats it rarely qualifies for many on the list.
In a statement Mr Cardownie said: “This is a vital election for Edinburgh and Scotland. If Scotland is to move towards Independence at this election we need to make the second list vote count by voting for Alba.”
Elected as a Labour councillor in 1988, he defected to the SNP in 2005. And after the 2007 elections, when the Nationalists went from one to 12 councillors, he led the party into a coalition with the Lib Dems, serving as deputy council leader for the next five years. The SNP's numbers jumped to 18 at the next elections in 2012 and Mr Cardownie kept the party in power by negotiating a new partnership with Labour. He stepped down from the group leadership in 2015 and stood down from the council at the last elections in 2017.
He writes a weekly column in the Evening News.
He said: “The fact is that an SNP vote while necessary in the constituency is a wasted vote on the list which hands seats to the pro-Union parties as we found in 2016 when the SNP got nearly 120,000 votes across Lothian and no seats.
“This time it has to be Alba for the list to ensure a greater number of Independence supporting MSPs are returned to the Scottish Parliament.”
Welcoming his support, Kenny McAskill who is heading up the Alba candidates in Lothian said: “Steve is highly respected in the City of Edinburgh. To have his support for Alba is a massive boost for our campaign to win list seats at the coming election.”