WASHINGTON — The Justice Department announced on Thursday that Donald B. Verrilli Jr., who won historic Supreme Court rulings for the Obama administration on its signature health care law and on same-sex marriage, would be stepping down as the nation’s top appellate lawyer.

Mr. Verrilli, 58, has been the solicitor general for five years, arguing the administration’s position before the justices during an unusual wave of contentious cases that drew attention far outside the legal world.

President Obama credited Mr. Verrilli in a statement with “winning landmark cases that moved America forward,” while Attorney General Loretta E. Lynch said in announcing his departure that “Don has been at the center of the foremost legal challenges of our time.”

Mr. Verrilli’s two most important wins will most likely be remembered as the Supreme Court’s 2012 decision upholding the constitutionality of the Affordable Care Act, and its decision last year declaring a constitutional right to same-sex marriage.