WASHINGTON — President Trump on Monday selected Judge Brett M. Kavanaugh, a politically connected member of Washington’s conservative legal establishment, to fill Justice Anthony M. Kennedy’s seat on the Supreme Court, setting up an epic confirmation battle and potentially cementing the court’s rightward tilt for a generation.

Presenting Kavanaugh at the White House, Trump described him as “one of the finest and sharpest legal minds in our time’’ and declared him a jurist who would set aside his political views and apply the Constitution “as written.’’

The nomination of Kavanaugh, 53, a federal appeals court judge, former aide to President George W. Bush, and onetime investigator of President Clinton, was not a surprise, given his conservative record, elite credentials, and deep ties among the Republican legal groups that have advanced conservatives for the federal bench.

But it will galvanize Democrats and Republicans in the months before the midterm elections. Justice Kennedy, who is retiring, held the swing vote in many closely divided cases on such issues as abortion, affirmative action, gay rights, and the death penalty. Replacing him with a committed conservative, who could potentially serve for decades, will fundamentally alter the balance of the court and put dozens of precedents at risk.

Judge Kavanaugh’s long history of legal opinions, as well as his role in some of the fiercest partisan battles of the last two decades, will give Democrats plenty of ammunition for tough questions. Nearly 20 years ago, working for the independent counsel Kenneth W. Starr, he laid out broad grounds to impeach Clinton — words that Democrats can now seize on to apply to Trump and the Russia investigation. Senator Mitch McConnell of Kentucky, who leads the barest of Republican majorities, had also expressed misgivings about his path to confirmation.

In choosing Kavanaugh, the president opted for a battle-scarred veteran of Republican politics but also someone with close ties to the Bush family — a history that aides to Trump said he viewed as a strike against him and had to overcome.

Before serving Bush in the White House, Kavanaugh worked for him in the 2000 presidential vote recount in Florida. When Bush nominated him in 2003 to the US Court of Appeals for the District of Columbia Circuit, Democrats complained that he was too partisan. He survived a contentious confirmation hearing and was confirmed in 2006.

In his remarks, Kavanaugh, who once clerked for Justice Kennedy, said he would “keep an open mind in every case.’’ But he declared that judges “must interpret the law, not make the law.’’

Democrats are still bitter that Republicans blocked President Obama’s nomination of Judge Merrick B. Garland to fill the last Supreme Court vacancy, created by the death of Justice Antonin Scalia in 2016. Republicans denied Garland a hearing, arguing that the right to name a justice ought to be left to Obama’s successor.

Trump chose Justice Neil M. Gorsuch, who has voted much as Justice Scalia had, leaving the court’s ideological dynamic basically intact. Replacing Justice Kennedy will be far more consequential, almost certainly thrusting Chief Justice John G. Roberts Jr., whose voting record has been more conservative than that of Justice Kennedy, into the crucial median position on the court.

For Trump, whose presidency has been marked by personnel upheaval, an uneven legislative record, and persistent questions over his ties to Russia, the nomination offers a chance for a clear victory — one that would leave a lasting imprint on one of the nation’s most cherished institutions. It also fulfills, for a second time, Trump’s promise to his political base to name conservative judges in the mold of Scalia.

As he did in choosing Gorsuch, Trump turned the selection process into a kind of Supreme Court sweepstakes, conducting a parade of interviews, promising a blockbuster choice, and stretching out his decision-making over a weekend at his golf club in New Jersey before announcing it in a prime-time appearance at the White House.

But there was less underlying drama than Trump’s theatrical approach suggested. As he did last time, the president chose from a list of two dozen candidates, carefully curated for him by the Federalist Society, which functions as a pipeline to supply conservatives to the federal bench.

Trump narrowed the list to four finalists: in addition to Kavanaugh, Judges Thomas M. Hardiman, Raymond M. Kethledge, and Amy Coney Barrett. All four are white, middle-age conservative federal appeals court judges. Three are Catholic; only Judge Kethledge is not.

While there are ideological differences among them — Barrett is an outspoken social conservative, while Kavanaugh, Kethledge, and Hardiman are viewed more as pro-business, law-and-order judges — all four have compiled uniformly conservative records.

One of the things that set Kavanaugh apart, aides to Trump said, was his Ivy League pedigree: He is a graduate of Yale and Yale Law School. He also impressed Trump during his interview, and was enthusiastically backed by the White House counsel, Donald F. McGahn II.

For Democrats, the nomination sets up a political battle they are likely to lose. While Republicans hold a razor-thin margin in the Senate — Senator John McCain’s absence because of his brain cancer reduces it to 50 seats — a handful of Democrats might vote for the nominee, particularly those running for reelection in states where Trump won in 2016 and is still popular.

Among Democrats facing that dilemma: Heidi Heitkamp of North Dakota, Joe Donnelly of Indiana, and Joe Manchin III of West Virginia. All three voted to confirm Gorsuch. Bob Casey, a Pennsylvania Democrat who is also up for reelection, made his intention to reject Trump’s choice clear hours before he even announced it.

“I will oppose the nomination the president will make tonight because it represents a corrupt bargain with the far right, big corporations, and Washington special interests,’’ Casey said in a statement.

However slim his odds of success, the Senate Democratic leader, Chuck Schumer of New York, framed the confirmation battle as a referendum on the issues most important to Democratic voters.

“Enormously important issues hang in the balance,’’ he said in the Senate before the announcement. “The right of workers to organize, the pernicious influence of dark money in our policy, the right of Americans to marry whom they love, the right to vote. Two issues of similar and profound consequence are the fate of the Affordable Care Act and a women’s freedom to make the most sensitive decisions about her body.’’

Republicans hope the appointment will mobilize their voters as well. But the choice of Kavanaugh is perhaps the most challenging of the four finalists, with lawmakers warning that his voluminous record could prolong the confirmation process, even past the November election.

McConnell told the president that Hardiman or Kethledge would have an easier path to confirmation.

McConnell has worried about his independent-minded Kentucky colleague, Senator Rand Paul, who has bitterly criticized the foreign policy of the Bush administration and might use that as grounds to hold up Kavanaugh’s nomination.