President Biden has approved a shake-up of the leadership of his campaign, and will dispatch a top White House aide to take over functional control of his re-election effort just as former President Donald J. Trump appears to be seizing control of the Republican primary contest to oppose him.

The aide, Jennifer O’Malley Dillon, who was the campaign manager for Mr. Biden’s 2020 campaign and has served as a deputy chief of staff in the White House since he became president, will move to the Biden 2024 headquarters in Wilmington, Del., and direct the campaign’s efforts, according to five people familiar with the discussions.

It is unclear precisely what title Ms. O’Malley Dillon will take at the campaign or when the announcement will be made, though it could come later this week. Julie Chávez Rodríguez, the campaign’s manager since shortly after it began in April, is expected to retain that title.

“Our campaign manager is and will continue to oversee the president’s re-election efforts, and this campaign will remain laser-focused on defeating Donald Trump and MAGA extremism at the ballot box this November,” said Michael Tyler, the campaign’s communications director.

The move formalizes a setup in which Ms. O’Malley Dillon has for months overseen the campaign’s direction from Washington.

When the Biden campaign held a December retreat for staff members at its headquarters, it was Ms. O’Malley Dillon who led the proceedings — not Ms. Chávez Rodríguez, according to two people who attended the session but were not authorized to speak publicly about it.

Donors, operatives, elected officials and other Democrats supportive of Mr. Biden have been increasingly worried about a campaign structure that had major and even minor decisions being made by White House aides and carried out by campaign personnel in Delaware.

In recent months, former President Barack Obama met with Mr. Biden at the White House and raised concerns about the bifurcated arrangement, according to an account of their discussion reported by The Washington Post.

The expected leadership change comes as the campaign is set to shift into a general-election posture and a more aggressive effort to contrast Mr. Biden with Mr. Trump, who won Iowa’s caucuses last week and held a significant polling advantage heading into the New Hampshire primary election on Tuesday against Nikki Haley, the former South Carolina governor who is his last major Republican rival.

Lisa Lerer contributed reporting from Manchester, N.H.