WASHINGTON — Vice President Mike Pence’s chief of staff will depart the White House in the coming weeks and will be replaced by a long-serving aide, in the first major staff change of his office, officials said on Thursday.

Mr. Pence’s chief of staff, Josh Pitcock, will be replaced by Nick Ayers, a veteran political operative from Georgia who has been working with the vice president for three years. Mr. Ayers was the chief political strategist for Mr. Pence, then the governor of Indiana, when President Trump chose the governor as his running mate.

More recently, Mr. Ayers has been one of the leaders of an outside group supporting the White House, America First Policies, which had been preparing a series of ads criticizing Senator Dean Heller, Republican of Nevada, for his anticipated no vote on the Senate’s bill to replace the Affordable Care Act, also known as Obamacare.

Mr. Pence, whose portfolio in the Trump White House is still developing, has told allies he would like to return…