The laws include the "Great Repeal Bill" to overhaul existing EU legislation and separate bills on customs, trade, immigration, fisheries and agriculture.
The queen said the "Great Repeal Bill" would repeal the European Communities Act, the 1972 legislation that enshrined Britain's membership of the European bloc.
"My government's priority is to secure the best possible deal as the country leaves the European Union," the queen said in the speech.
She said her government would seek "to build the widest possible consensus on the country's future outside the European Union", amid divisions within her own cabinet over the best strategy.
Britain voted to leave the European Union in a referendum last year but there is growing opposition to the government's "hard Brexit" approach of cutting immigration at the expense of trade ties.