The 20-year-old full-back joins the Tigers from the Airtricity Premier Division title contenders, with the fee being paid reported to be in the region of £200,000
The 20-year-old has impressed for the Leesiders this season, helping them to second place in the Airtricity Premier Division, attracting the attention of Manchester United, Arsenal, and many others.
Both Brighton and Hove Albion and Hull had bids accepted for the full-back, with a fee reported to be around £200,000 agreed with the Tigers.
Manager Steve Bruce confirmed the transfer after his side's 2-1 defeat to Aston Villa on Sunday, telling the press: "Lenihan is done and dusted. He's one for the future."
The Leesiders also announced the transfer, with chairman Pat Lyons praising the right-back's impact at the club.
"We would like to wish Brian the best of luck in the next stage of his career," he enthused.
"Since he joined us, Brian has been a credit to his family and to his schoolboy club, College Corinthians; showing a fantastic attitude and excellent ability, which I am sure will see him progress far in the game.
"As a club, we never want to see our best players depart, however we are pleased that we have reached what we believe to be a fair and reasonable agreement with Hull for his transfer and that Cork City stands to benefit further should Brian continue to progress as we all expect him to do."