“Judge Walker was an unrelenting defender of Justice Kavanaugh during the left’s unprecedented smear campaign,” Carrie Severino, the president of the conservative Judicial Crisis Network, said on Twitter after his nomination. “I expect Walker to bring similar courage with him to the DC Circuit as he defends the rule of law.”

Judge Walker is a graduate of Duke University and Harvard Law School and had worked as an appellate lawyer in the Washington office of Gibson, Dunn & Crutcher before returning to Louisville to practice law and teach. He is a member of the Federalist Society, the conservative group that has been central to the extremely successful push by the Trump administration, in concert with Mr. McConnell, to place scores of conservatives on the federal courts.

In his writings, Judge Walker has exhibited a strongly conservative view. In one article, he labeled the Supreme Court decision upholding the Affordable Care Act as “catastrophic.” Defending Justice Kavanaugh, Judge Walker hailed a conservative judicial revolution that he said would bring “an end to affirmative action, an end to successful litigation about religious displays and prayers, an end to bans on semiautomatic rifles and an end to almost all judicial restrictions on abortion.”

In opposing the confirmation last year, Senator Chuck Schumer, Democrat of New York and the minority leader, pointed to Judge Walker’s lack of experience and said the only reason for his nomination seemed to be “his membership in the Federalist Society and his far-right wing views on health care, civil rights, and executive power.”

Judge Walker would succeed Judge Thomas B. Griffith, who was nominated in 2004 by President George W. Bush after Senate Democrats filibustered the nomination of Miguel Estrada and intensified the fight over judicial confirmations that is still underway. Judge Griffith announced last month that he would step down in the fall.

Judge Walker’s confirmation would not immediately change the balance on the court, which now consists of seven judges nominated by Democratic presidents and four by Republicans. He would be the third judge Mr. Trump has placed on the court.

Mr. McConnell has emphasized that he intends for the Senate to continue confirming judges through the end of the year, adopting the motto of “leave no vacancy behind.” With openings diminishing, Mr. McConnell and other Senate Republicans have been reaching out to Republican-nominated judges eligible for retirement to sound them out about their plans.