Mr Findlay was in a three-way contest for the position with Jim Murphy and Sarah Boyack last December but said he will not be a candidate this time.
He was part of Mr Murphy’s shadow cabinet but resigned last week, citing the party’s “disaster” in the general election in Scotland.
In a statement today he said: “The last week has been a traumatic time for everyone in the Scottish Labour Party. We now need to get on with the urgent task of rebuilding our organisation, the morale of party members and the policies we need to restore the faith of the voters in the run up to the 2016 Scottish Parliament elections.
“I hope to play my full part in that process but I also want to make it crystal clear that I will not be a candidate in the election for the position of Scottish Labour leader.
“I hope that we can now move ahead as quickly as possible in electing a new leader who will begin the fightback by rebuilding a confident, effective Labour party, proud of our values whilst offering hope and a positive vision for the future.”