Brexit Secretary David Davis told the Exiting the EU Committee: "I think I'm right in saying that we're expecting Royal Assent tomorrow."
The PM has said she plans to invoke Article 50 of the Lisbon Treaty by the end of March.
Mr Davis was questioned by the MPs about the negotiations that will follow Article 50.
The government says it can complete separation talks and a trade deal "in parallel" within two years, but EU leaders say the two negotiations have to take place separately.
Mr Davis said this would be the "first formal conversation" he would have with chief EU negotiator Michel Barnier.
He said he was confident other countries would agree to a free trade deal with the UK even if every national Parliament's approval was required.
"Every country will have an interest," he said.
The legislation allowing Theresa May to trigger Brexit will be rubber-stamped on Thursday, MPs have been told.