He will take up the role in the new year, after the departure of Michael Sharpe last week, until the Scottish Parliament elections in May.
Mr Smith, who currently works with the GMB union, said the vote next year would be an important one for the party.
“The events of the last year have shown more than ever how important it is that the voices of working people are heard in Scottish politics,” he said.
“The campaign ahead is our chance to take our message to the people of Scotland, but also for all of the talented and committed people already in our party to be included and to get involved.
“Working together, I believe we can see our party growing again and I will also work hard to again make Scottish Labour a welcoming place for all who share our values.”
Scottish Labour leader Richard Leonard said Mr Smith was respected across the party.
"I am looking forward to working with Drew to gear up the Party for next year’s election,” he said.
"He is an experienced campaigner and widely respected across the Labour movement.
"Together we will ensure that we have a positive and distinctive Scottish Labour message to take to the people of Scotland. I am delighted that he has agreed to take up this post.
"Now more than ever we need a Scottish Parliament and Scottish Government which is dedicated to tackling the public health crisis and the jobs and economic crisis which the country faces.”