The speech, on Wednesday, will set out the UK government's programme following the general election.
Theresa May said she will work with Parliament, business and the devolved administrations "to ensure a smooth and orderly withdrawal" from the EU.
But First Minister Carwyn Jones warned of a "constitutional crisis" should she "disrespect devolution" over Brexit.
Mrs May said the government's programme was "about recognising and grasping the opportunities that lie ahead for the United Kingdom as we leave the European Union".
"It is about delivering a Brexit deal that works for all parts of the UK," she said.
Mrs May added: "We are clear that we are going to see Brexit through, working with parliament, business, the devolved administrations and others to ensure a smooth and orderly withdrawal.
"This will, therefore, be a busy legislative session with a number of bills geared towards making a success of Brexit."
However, Mr Jones urged the prime minister to "put the UK economy above political self-interest" and reconsider plans for a "hard Brexit for which she has no mandate", after losing her House of Commons majority in the general election earlier this month.
"We are ready and willing to work with the UK government and the devolved administrations to agree common approaches - through discussion, not diktat - to prevent friction within our own internal market," he said.
Last Thursday, Mr Jones unveiled a blueprint to overhaul relations between the governments of the four nations after the UK leaves the European Union.
"Last week we set out exactly how this can be achieved in our policy paper on Brexit and devolution," he said.
"However, if the prime minister disregards our efforts to work together and, instead, chooses to disrespect devolution and constrain the devolved nations, she will bring about a constitutional crisis that will damage the union."
Mr Jones said businesses were "crying out for clarity" while "our economy needs certainty".
BBC Wales parliamentary correspondent David Cornock said the Queen's Speech was unlikely to include a bill to scrap the Severn bridge tolls.
"UK government sources say this is because they are likely to be scrapped by secondary legislation," he said.
Mrs May promised to abolish the tolls if the Conservatives won the general election.
The prime minister says the Queen's Speech will help deliver a Brexit which will work for all parts of the UK.