LONDON — It was the subject of anguished national debate, multiple cliff-hanging votes in Parliament, a landmark court decision and two extraordinary elections. Yet, when the British Parliament voted Friday to advance Prime Minister Boris Johnson’s Brexit plan, it had all the drama of a rubber stamp.

To some extent, that’s what it was: With Parliament now firmly under the grip of Mr. Johnson and his Conservative Party, following their landslide victory in the general election last week, the days of monumental, or even trivial, challenges to the government in the House of Commons are over.

By a count of 358 to 234, Parliament voted to advance the withdrawal agreement that Mr. Johnson negotiated with the European Union in October, paving the way for Britain to leave at the end of next month.

The House of Lords must still give its imprimatur, but it is unlikely to obstruct a bill that was enshrined in the manifesto of the Conservative Party and formed the centerpiece of Mr. Johnson’s winning campaign.

“We come together as a new Parliament to break the deadlock and finally to get Brexit done,” Mr. Johnson said in Parliament, joking that he had the votes to wrap up the entire debate by lunchtime or, as he put it, a “late lunch.”

The prime minister appealed for unity in the wake of the election, arguing that the completion of Brexit provided an opportunity for Britain to put behind it the tribal feuds of the last three and a half years. “This is the time when we move on and discard the old labels of leave and remain,” Mr. Johnson said.

Still, there were a few of the fiery exchanges that became familiar during more than two years of debate over Brexit. The Labour Party’s vanquished leader, Jeremy Corbyn, opposed the plan, fuming that it was a blueprint for deregulation and a predatory trade deal with the United States.

“We warned before the general election that the prime minister’s Brexit deal was a terrible deal for our country and we still believe it is a terrible deal today,” he said.

Instead of another knife-edge vote, however, this was a foregone conclusion.

With an 80-seat majority behind him, Mr. Johnson removed provisions from the bill that might have placated his opponents but limited his room for maneuver. He played to the gallery of Conservative lawmakers sitting behind him in the chamber, ruling out, with characteristic flourish, the possibility of extending a transition period for trade talks with the European Union that is scheduled to end in December 2020.

He further reminded lawmakers that it then grew back, “only to be pecked out again in the cycle repeated forever.”

While there is no longer any debate over whether Britain will leave the European Union, members of the opposition insisted there should still be a debate over how it leaves. The details of a trade agreement with Brussels are still to be hashed out, and lawmakers said they would oppose a deal that diverged radically from the European Union’s single market and regulations.

They noted that although the Conservative Party piled up a big majority in Britain’s first-past-the-post electoral system, parties that either opposed Brexit or had misgivings about it actually won a majority of the vote.

“Boris Johnson got 43 percent of the vote,” said David Lammy, a Labour Party lawmaker from London, on Twitter. “It is a mandate to govern, but not to impose a hard Brexit that destroys jobs, takes away our rights, and leaves the UK isolated in the world.”

Despite the anticlimactic nature of the vote, it was nevertheless a landmark, drawing to an end a tumultuous period that brought Mr. Johnson to power but eviscerated the careers of many of his colleagues in Parliament.

The former prime minister, Theresa May, lost her post over Brexit. Mr. Corbyn, who is shouldering much of the blame for Labour’s worst performance in a general election since 1935, will soon join her on the backbenches.

At least Ms. May and Mr. Corbyn still hold their seats in Parliament. The leader of the centrist and pro-European Liberal Democrats, Jo Swinson, was ejected by voters in her constituency after a brief and disastrous spell as leader, when she campaigned on the idea of reversing Brexit.

So, too, was Nigel Dodds, who had been Westminster leader of the Northern Irish Democratic Unionist Party, and whose political fortunes symbolized the twists and turns of the Brexit roller coaster.

For two years, after the general election in 2017, Mr. Dodds held the balance of power at Westminster. He propped up Mrs. May’s Conservative minority government and helped kill her Brexit plan by withdrawing support for it from his bloc of 10 Democratic Unionist lawmakers.

When Mr. Johnson became prime minister last summer and renegotiated the Brexit agreement, the deal became worse from the perspective of the Democratic Unionists because it now requires checks on goods moving between Britain and Northern Ireland. In the election, voters dumped Mr. Dodds from his seat in North Belfast, one of two seats lost by the party.

Many other famous faces are missing from the new Parliament.

Philip Hammond, who served as chancellor of the Exchequer under Mrs. May, was expelled from the Conservative Party by Mr. Johnson for resisting his Brexit policy. He did not run again for his seat.

Nor did others who were ejected from the party, including Nicholas Soames, a grandson of Winston Churchill, though he was later reinstated, and Rory Stewart, who is now a candidate for London mayor.

“The political landscape has completely changed,” said Vernon Bogdanor, a professor of government at King’s College London. There could be another decade of Conservative rule, he said, because the Labour Party will need two general elections to recover its standing with voters.

Mr. Bogdanor said that the government still faced an uphill struggle to negotiate a trade agreement with the European Union. And the government will have to deal with increasingly restive outposts in Scotland and Northern Ireland, where strong majorities oppose Brexit and may view it as a pretext to break away.

Still, he said, “The long debate on Europe will finally have come to an end.”