By Jessica Toonkel and Patience Haggin

When Comcast Chairman Brian Roberts decided a few weeks ago to pursue a spinoff for the company's media and entertainment business, there was just one question: Who would run the cable and broadband operations that remained?

He offered the job to his longtime friend and former finance chief Michael Angelakis, who agreed to it during a four-hour lunch at a diner near Philadelphia, where Comcast is based. "This industry has been kind of in my blood for a long time," Angelakis said in an interview.

In bringing back Angelakis, Roberts, 67 years old, is picking an executive steeped in cable and broadband who is part of a small circle of trusted advisers, said people close to both men.

Angelakis, 62, is known as an ambitious, levelheaded and disciplined dealmaker with an entrepreneurial bent. He was an architect of Comcast's acquisition of NBCUniversal and, for the past decade, has run investment firm Atairos with Comcast's backing.

"He is bold, and he isn't afraid to take risks," said Barry Diller, chair of People Inc., who has known Roberts and Angelakis for years. "That is what the enterprise needed."

Angelakis will be taking the helm of a connectivity business that has long generated the bulk of Comcast's revenue, bringing in north of $80 billion last year. But it is a business that faces growing headwinds as new players such as mobile carriers have entered the home-internet market and Elon Musk's Starlink satellite company has also made inroads in connectivity. Comcast has lost domestic broadband customers for 12 consecutive quarters.

The new, slimmed-down Comcast will also house the company's cable operations, which have been bleeding subscribers for years as consumers migrate to digital streaming services.

Angelakis grew up in Peabody, Mass., and attended an area prep school before earning an undergraduate degree at Babson College. While still in his 20s, he came to oversee a media and communications portfolio at the bank Manufacturers Hanover Trust, which is today part of JPMorgan Chase. He also led a small cable company and a small telecom company.

He joined private-equity firm Providence Equity Partners in 1999, where he became a managing director, before moving to Comcast in 2007 to become chief financial officer.

While Roberts raised the idea of buying NBCUniversal from General Electric, Angelakis was a crucial player in negotiating the deal. He remained thoughtful and calm throughout the process, said Steve Burke, the former head of NBCUniversal.

At one point when talks began to fray, Angelakis traveled to the Cape Cod summer home of his GE counterpart to hash out a term sheet. The deal was announced in 2009; Comcast took a 51% stake in NBCUniversal in 2011 and bought the other 49% two years later.

As CFO of Comcast, he often was able to smooth over tensions that Roberts sometimes caused with other companies with his tough negotiating stance, said people familiar with the situation.

Roberts and Angelakis grew so close that when Angelakis decided he wanted to go out on his own after eight years at Comcast, Roberts had the company back his new investment firm, Atairos. Angelakis also put his own money in Atairos, whose holdings include Arcis Golf, Life Time fitness clubs and Opry Entertainment Group.

Angelakis served on the board of the Federal Reserve of Philadelphia, including as its chairman in 2016. He currently sits on the boards of American Express, Exxon Mobil and Lucky Strike Entertainment, an Atairos holding.

For Angelakis, the return to Comcast represents a chance to run a public company with the complete trust of the controlling shareholder and a "meaningful platform," said Hollywood executive Peter Chernin, who has known him for more than 20 years. "It will be really interesting to see what he does with it."

Write to Jessica Toonkel at jessica.toonkel@wsj.com and Patience Haggin at patience.haggin@wsj.com