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.

The nomination of Judge Kavanaugh, 53, a federal appeals court judge, former aide to President George W. Bush and onetime investigator of President Bill Clinton, was not a huge 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 issues like 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 Mr. Clinton — words that Democrats can now seize on to apply to Mr. 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.