The "scale and complexity" of the EU (Withdrawal) Bill is complicated by the fact that much depends on the outcome of Brexit negotiations, it says.
The Lords Constitutional Committee says, as it stands, the bill is "constitutionally unacceptable".
It will be debated by peers for the first time on Tuesday.
The UK is due to leave the EU in March 2019, and the EU (Withdrawal) Bill is a key part of the government's Brexit strategy.
It aims to end the supremacy of EU law, which would be copied into UK law in order to ensure a smooth transition on Brexit day.
But committee chairwoman Baroness Taylor said: "We acknowledge the scale, challenge and unprecedented nature of the task of converting existing EU law into UK law, but as it stands this bill is constitutionally unacceptable."
The bill passed through the Commons after it faced hundreds of attempts to change its wording and suffered one government defeat.
It begins two days of debate in the Lords on Tuesday.
The Lords Constitution Committee said the aim of transposing EU law into UK law in time for Brexit was complicated by its complexity and because "in many areas the final shape of that law will depend on the outcome of the UK's negotiations with the EU".
It said a new "retained EU law" category would create uncertainty and ambiguity, and powers to allow ministers to amend regulations without full parliamentary scrutiny were "overly-broad".
And without agreement from Holyrood and Cardiff Bay on devolution issues there could be "significant constitutional repercussions", the peers warned.
"The bill is therefore fundamentally flawed from a constitutional perspective in multiple ways," the report said.
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