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Last month, the Fife MSP was suspended from the post following allegations that he had sent abusive text messages to a former partner.
Mr Rowley rejected the allegations and said he would work to clear his name.
On Saturday he said the party's investigations panel had discharged the case but he was disappointed he did not have the opportunity to respond.
Lesley Laird will take over the role of deputy leader on an interim basis.
Mr Rowley, who was interim leader of Scottish Labour before Richard Leonard was appointed, had referred himself to the party's investigation unit, and announced he would step aside from the leadership after claims were published in The Scottish Sun.
In a statement released on Saturday, he said: "Today, I have informed Richard Leonard that I do not intend to resume the role of deputy leader of the Scottish Labour Party.
"I am pleased the panel has discharged the case which I referred to them, but I am disappointed that they were unable fully to investigate - and I to have the opportunity to answer - the allegations, which relate to the acrimonious end to a relationship nearly five years ago.
"This means the only opportunity to do so would have been through the media and I am not prepared to cause that distress to my family.
"I am in politics to fight for social, political and economic change to improve the lives of working people. I will continue that work as a Labour MSP for the region of Mid Scotland and Fife."
Scottish Labour leader Richard Leonard said: "Following on from Alex Rowley's decision to resign from the position of deputy leader of the Scottish Labour party, I have asked Lesley Laird to assume the position on an interim basis.
"I have spoken to Alex and for the sake of his family he has decided to step down from this important role.
"He informs me that it is a decision he made some time ago. He is a loyal and experienced member of the Labour group in the Scottish Parliament and will continue to play a part in rebuilding the Labour Party in Scotland."
Mr Rowley, who previously served as election agent for former prime minister Gordon Brown, stood in as the Scottish Labour leader when Ms Dugdale resigned in August.
While the investigation took place, Scottish Labour announced that Mr Rowley would be suspended from the Labour whip in the Scottish Parliament.
His position as interim leader had previously been questioned when he was caught on tape backing Mr Leonard as the "best candidate".