MSP Keith Brown, councillor Christopher McEleny and activist Julie Hepburn are bidding to replace Angus Robertson in the role.
Mr Brown, Scotland’s economy secretary, is the highest profile figure in the race, while Mr McEleny, leader of the SNP group on Inverclyde Council, competed in the previous depute leadership election.
While not an elected representative, Ms Hepburn is well known within the party.
The depute leader role became available when Mr Robertson stepped down in February after losing his Westminster seat in last year’s general election.
MSP James Dornan pulled out of the race earlier this month, stating he intended to focus on fighting sectarianism. He has backed Ms Hepburn instead.
Several senior SNP MPs, including Westminster leader Ian Blackford, previously ruled themselves out of the running.
The candidates will now take part in a series of hustings events across the country.
Ballots will open on May 18, with the election conducted using the single transferable vote system.
Voting closes on June 8, with the winner announced at the SNP conference in Aberdeen later that day.