Lumen Technologies Inc. plans to sell a swath of its U.S. telecommunications network to Apollo Global Management Inc. for $7.5 billion including debt, officials from the companies said.

The investment giant will carve out some of Lumen’s so-called incumbent local exchange carrier assets, a collection of telephone and broadband infrastructure that covers more than 6 million residential and business customers across 20 states, mostly in the U.S. Midwest and Southeast. The deal value includes $1.4 billion of assumed debt.

Lumen’s remaining operations will focus on large business clients, which generate most of its revenue, as well as home-broadband subscribers in 16 states including Colorado, Florida and Washington.

The new Apollo-backed company, which aims to accelerate the business’s shift from older copper lines to high-speed fiber-optic technology, will be led by Verizon Communications Inc. veterans Bob Mudge, Chris Creager and Tom Maguire, who together built out Verizon’s fiber-based, Fios service.

Lumen Chief Executive Jeff Storey said the company is shifting its focus to consumer markets it considers good upgrade candidates for its own fiber business.

“If you look at the markets that we’re transferring to Apollo, these are markets that Lumen would not have invested as heavily in,” he said in an interview. “Apollo will put the investment into these markets that we believe they can sustain.”

The sale is the latest course change for Lumen, the company known as CenturyLink until its 2020 rebranding. CenturyLink was among the few remnants of the former AT&T monopoly to survive into the 21st Century, though it avoided copying peers’ pursuit of wireless customers and focused its attention on landlines. In July, Lumen said it was selling its Latin American assets to infrastructure investor Stonepeak Partners LP for $2.7 billion.

CenturyLink grew bigger after it agreed in 2016 to merge with Level 3 Communications, a Denver-area network operator geared toward large business customers. The combination yielded billions of dollars in savings and tax advantages, though executives faced challenges stitching together the business cultures of CenturyLink, based in Monroe, La., and the operations inherited from Level 3 in Broomfield, Colo.

For Apollo, the Lumen deal plays into a thesis the firm has developed with the new company’s executives around the need for fiber-based broadband to be expanded in the U.S. While fiber is a superior consumer broadband technology, many potential providers of fiber have lacked the access to capital to upgrade their sprawling networks, according to Aaron Sobel, the Apollo partner who led the deal. As a standalone company, the new entity won’t have other capital needs that take priority.

“It’s very difficult to carve out these states from a large telco,” Mr. Sobel said. “You’re dealing with a business that is legacy and theoretically declining and returning it to growth.”

Write to Drew FitzGerald at andrew.fitzgerald@wsj.com and Miriam Gottfried at Miriam.Gottfried@wsj.com