The field was announced in Indianapolis.
The top-ranked Tar Heels (32-2) are the No. 1 seed both in the East and overall.
UNC beat Clemson 86-81 in the ACC Tournament title game Sunday.
The Tar Heels will face the winner of Tuesday's contest between Coppin State and Mount Saint Mary's in their NCAA opener Friday in Raleigh, N.C.
Memphis (33-1) is the top seed in the South and will play Texas-Arlington Friday in Little Rock, Ark.
UCLA (31-3), the West's No. 1 seed, plays Mississippi Valley State Thursday in Anaheim, Calif.
Kansas (31-3), the Midwest's top seed, plays Portland State Thursday in Omaha. The Jayhawks beat Texas 84-74 in the Big 12 Tournament final Sunday.
"In people's minds, when you are a one seed, they think you are one of the best four teams in the country," Kansas Coach Bill Self said. "Being a No. 1 seed was not the goal. The goal was to have a favorable path, and while there are no easy paths, it's nice to stay in the Midwest Region."
Memphis (Conference USA) and UCLA (Pac-10) had won their conference tournament finals Saturday.
Neither two-time national champion Florida nor Ohio State was chosen, making it the first time in nearly 30 years the schools that played in the national title game the previous season failed to qualify.
Both schools were picked for the NIT field, which was unveiled Sunday night.