WASHINGTON — After weeks of uncertainty atop the Department of Veterans Affairs, President Trump dismissed its secretary, David J. Shulkin, on Wednesday and announced he would replace him with the White House physician, Dr. Ronny L. Jackson, a rear admiral in the Navy.

If confirmed, Dr. Jackson, a career Naval officer who has no real experience running a large bureaucracy, would inherit a set of challenges that have bedeviled Democratic and Republican administrations alike. The department, the federal government’s second largest, has been burdened for years by aging infrastructure, an inefficient health care system and an unwieldy 360,000-person work force.

He could also quickly face crucial, multibillion-dollar decisions over the replacement of its outdated computerized records system and legislation that would ease the rules around veterans seeking private health care at government expense.

The announcement punctuated what has been a rapid fall from favor for Dr. Shulkin, a politically moderate former hospital executive who delivered Mr. Trump a string of bipartisan legislative victories at a time when he was struggling to find them. But in his final weeks, he struggled to fight off attempts by more conservative administration officials to have him removed and was dogged by an unflattering inspector general report on his overseas travel that undermined his relationship with the president.