Also getting the nod for enshrinement at Canton, Ohio, were Coach Bill Parcells and senior nominees Curley Culp and Dave Robinson.
The announcements were made in New Orleans on the eve of Super Bowl XLVII, pitting San Francisco against Baltimore.
Carter, an eight-time Pro Bowl selection with the Philadelphia, Minnesota and Miami from 1987-2002, made it in his sixth year as a finalist. He compiled 1,101 receptions with 13,899 yards and 130 touchdowns over his 16-year career.
Ogden earned 11 Pro Bowl selections during his 12 NFL seasons as an offensive lineman, all spent with Baltimore. He was the team's first-ever draft pick in 1996.
Allen, another offensive lineman, also earned 11 trips to the Pro Bowl while playing 12 seasons with Dallas.
Sapp -- a seven-time Pro Bowl pick at defensive end -- played for Tampa Bay and Oakland from 1995-2007, and was named the 1999 NFL Defensive Player of the Year with the Buccaneers.