The Hall of Fame's 39-member Board of Selectors made their choices after meeting in Detroit, the day before Super Bowl XL between the Pittsburgh Steelers and Seattle Seahawks.
Aikman, 39 and now an NFL television analyst, won three Super Bowls with the Cowboys. Selected first overall in the 1989 draft out of UCLA, he started all 165 games he played for Dallas and is the franchise's all-time leader with 32,942 passing yards and 165 touchdowns.
White, who died in December 2004 at the age of 43, held the all-time record with 198 sacks -- a mark since surpassed -- when he retired in 2000. After two years in the USFL, he played for the Philadelphia Eagles and Green Bay Packers from 1985-98. He came out of retirement in 2000 to play with the Carolina Panthers.