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 five were jailed in September for raping a Finnish woman during a World League tournament in Tampere.
The appeals court in the south-western city of Turku reduced the five-year sentences handed down to four of them.
The longest of the revised prison terms is that of Osmany Uriarte Mestre - four years. Luis Sosa Sierra was acquitted.
Ricardo Calvo Manzano will now serve three-and-a-half years, team captain Rolando Cepeda Abreu two-and-a-half years and Alfonso Gavilan one year and three months.
They were detained in the southern Finnish city on 2 July after a woman said she had been raped at a hotel. The men denied the accusation.
The team had been taking part in a tournament ahead of the Rio Olympics when the rape took place at their hotel.
Eight men were originally held. Two were released soon afterwards.
In September the Tampere court heard that two of the players had met the woman in a nightclub in the hotel basement. She later went to the room of Uriarte Mestre and consented to sex.
However, Uriarte Mestre was then said to have texted the other men without the woman's knowledge. They entered the room and subjected her to a lengthy ordeal and held her by the hair to prevent her leaving.
When she was eventually allowed to leave, she complained to the hotel receptionist who called police.
The Cuban players were found guilty of aggravated rape and ordered to pay â‚¬24,000 (Â£21,076; $27,383) in compensation to the victim.
As the allegations emerged, two of the team coaches were sacked.
Despite its depleted squad, Cuba fielded a team in Rio and lost all five of its matches.
The legislation allowing Theresa May to trigger Brexit will be rubber-stamped on Thursday, MPs have been told.
[NEXT_CONCEPT]
A Finnish court has cut the jail terms of four members of Cuba's national volleyball team found guilty of rape, and released a fifth.