The EU Withdrawal Bill will see these initially go to Westminster before the UK Government moves to return powers to Holyrood and the other devolved nations.
The Scottish Government has branded the move a "power grab" and Mr Leonard said today there is a "cast iron case" for the controls to go straight to Holyrood.
Asked on BBC Radio Scotland's Good Morning Scotland if the 111 powers should go to Scotland, he said: "Yes. I'm concerned and I think the Labour party at Westminster has expressed this concern that the way in which the Tory Government are seeking to return powers to the UK is extremely dubious.
"I do support those who are calling for devolved powers to come to the devolved Scottish Parliament."
Mr Leonard, who was elected Labour leader on Saturday, said this should mean all 111 disputed powers. This includes key responsibilities over areas like fishing and farming which should rest with Holyrood in lie with the terms of the Scotland Act.
And he added: "I also think there needs to be an examination of whether some of these other powers which are being repatriated should rest at a UK level or should rest at a Scottish level.
"But I certainly think when it comes to key devolved areas like fisheries and agriculture there's an absolute cast iron case in my view for these powers and responsibilities to be transferred straight to the Scottish Government and in the end to the Scottish Parliament too."
The UK Government has insisted that Brexit will eventually lead to a "powers bonanza" for Holyrood but insisted it must take time in the early stages of Brexit to allocate which powers should remain reserved to protect the UK internal market.