She picked Mr. Benjamin, a Black former state senator from Harlem, as her running mate in August in an effort to broaden her appeal among city voters. She had occupied the position herself until former Gov. Andrew M. Cuomo’s sudden resignation.

After Mr. Benjamin’s tenure ended in his arrest, undermining the governor’s promises to clean up corruption in Albany, she was determined to pick a lieutenant governor without any red flags. She asked Elizabeth Fine, the counsel to the governor, and Marty Mack, the appointments secretary, to oversee a team of lawyers scrubbing candidates’ backgrounds.

Governor Hochul considered a handful of officials of color, though it appears she did not constrain her options to those hailing from the downstate region. The selection process was kept remarkably under wraps, devoid of the leaks that defined Ms. Hochul’s first, flawed search for a second-in-command.

A former Rhodes scholar and corporate lawyer, Mr. Delgado offered considerable political attributes. He has twice been elected in one of the most competitive swing districts in the country. He has faced a deluge of opposition research spread by Republican opponents who tried to brand him as a “big-city rapper.” He is also a prolific fund-raiser, with nearly $6 million in his House campaign account, which can be used for the lieutenant governor race.

“They got burned on picking Brian Benjamin,” said John Faso, a former Republican congressman who lost to Mr. Delgado in 2018. “Now they’ve got a guy who went through a very competitive race in 2018 and doesn’t have the baggage that other candidates might have.”

In Congress, Mr. Delgado has largely avoided the kind of partisan fights that dominate cable news and rarely, if ever, speaks with reporters. He has served on the agriculture, small business and transportation committees and has one of the most moderate voting records of any Democrat.

In the primary for lieutenant governor, a largely ceremonial role entrusted with few statutory duties, Mr. Delgado will face two opponents, both Latina women: Diana Reyna, a former New York City Council member, and Ana María Archila, a progressive activist. How voters will receive his last minute entrance into the lieutenant governor’s race is less assured.