"The British people have made the decision to leave the EU... so today we have introduced a bill in parliament which will allow us to formally trigger Article 50 by the end of March," said Brexit minister David Davis.
The two clause "European Union Notification of Withdrawal Bill" asks parliament to give May authority to start the formal mechanism by which Britain will leave the bloc.
The government said MPs would get their first chance to debate and vote on it on Tuesday and Wednesday next week.
May's government was forced to go to parliament following a landmark Supreme Court ruling this week that rejected its argument that executive powers allowed it to proceed.
The ruling Conservatives have a small majority in the House of Commons and the bill is expected to get the go-ahead from MPs, although opposition parties have said they plan put forward amendments that could slow it down.
Davis said he hoped that parliament would "respect the decision taken by the British people and pass the legislation quickly," arguing that MPs had supported holding the referendum in the first place.
House of Commons leader David Lidington told parliament that the bill's third and final reading in the House of Commons -- followed by a final vote by MPs -- would be on February 8.
The bill will then pass to the upper House of Lords, where progress is less certain as the government has no majority there and no control over the timing.
"The Lords will not block or wreck the bill but they will want to give it proper scrutiny, especially if they think the scrutiny in the Commons has been inadequate," Robert Hazel and Alan Renwick from University College London's Constitution Unit said.
If approved by the House of Lords, the bill would then have to be signed off by Queen Elizabeth II before May can trigger Article 50 of the EU's Lisbon Treaty -- the formal process for leaving the bloc.
May has said she is confident she will be able to stick to her timetable of triggering Article 50 by the end of March at the latest and the government has said it hopes to start Brexit talks before the summer.
Britain voted to leave the European Union in a referendum on June 23 last year following a bitter campaign and divisions have persisted since then.
A majority of Britain's 11 Supreme Court judges on Tuesday ruled that withdrawing from the EU meant there would have to be changes in Britain's domestic laws and therefore parliament had to be involved.
There were shouts of "disgraceful" from MPs as the government outlined its rapid timetable for the bill.
The main opposition Labour Party has said it is planning amendments including a clause calling for the protection of workers' rights, while the Scottish National Party wants to put forward dozens of changes.
May's Conservative government currently has a working majority of 16 in the 650-member parliament.
The bill came as official data showed Britain's economy grew solidly in the final months of last year, even as it prepares for a difficult departure from the EU.
Gross domestic product expanded 0.6 percent between October and December, matching growth during the previous two quarters, the Office for National Statistics said.
For 2016 as a whole, British growth reached 2.0 percent, a decline from the previous year's increase of 2.2 percent.
The economy has performed better than expected since the Brexit vote, though analysts have said they expect a more difficult 2017.