The team on Monday also signed swingman Glenn Robinson III to a three-year deal and completed an undisclosed deal with second-round pick Rakeem Christmas.
Allen agreed to a multiyear deal worth $3 million annually this month. He has averaged 5.0 points and 4.8 rebounds in a five-year career.
Whittington played in 20 games last season after making the roster as an undrafted free agent. He was expected to re-sign after competing on Indiana's summer league team.
Robinson played in high school in Indiana and starred at the University of Michigan before leaving school early. His father, Glenn, was the No. 1 overall pick in the 1994 draft.
Christmas, a forward, was acquired in a trade with Cleveland last week.