Nominations for the post closed at noon on Monday with Ms Laird the only candidate nominated for the job.
Scottish Labour had been hunting for a new deputy leader after Alex Rowley stepped down from the post in December, after allegations were made about his private life.
Ms Laird defeated the SNP to win the Kirkcaldy and Cowdenbeath constituency - which was previously held by Gordon Brown - in the 2017 snap general election.
She will be formally confirmed as Scottish Labour’s new deputy leader after a meeting of parliamentarians and councillors in the coming days.
The MP said: “I’m ready to get on with the job of holding the Tory and SNP governments to account and outlining a positive vision of what a Labour government can do in Scotland and across the UK.
“The 2017 general election saw Labour win seats and slash majorities across Scotland. The next general election will see Scotland help deliver a Labour government that works for the many, not the few.”
Scottish Labour leader Richard Leonard said: “Scottish Labour is ready to deliver real change for people across Scotland, with strong teams at Holyrood and Westminster.
“Lesley will be a great voice for our members and our movement, to make the case for the economic and social transformation Scotland so desperately needs.
“Together we will build a Labour Party which appeals to all people of goodwill who want justice, equality, co-operation and real change.”