Iran international Ghoochannejhad, 28, scored five goals in 42 appearances after joining the Addicks in 2014.
Former Juventus defender Motta, 30, featured 12 times following his move to The Valley in February.
Marko Dmitrovic, Alou Diarra and Callum Harriott have triggered one-year extensions to their current deals.
Meanwhile, the south-east London club have offered a new contract to 20-year-old goalkeeper Dillon Phillips.
Development squad players Zak Ansah, Alex Kelly, Ayo Obileye, Josh Staunton and Joe Pigott will also leave Charlton, who finished 22nd in the Championship this season and dropped back into League One following four years in the second tier.
Jose Riga left his position of head coach following the final game of the season and the Addicks are yet to appoint a new boss.
Northampton's Chris Wilder was approached to succeed the Belgian but turned the job down and joined Sheffield United instead.
Forward Reza Ghoochannejhad and full-back Marco Motta will leave relegated Charlton Athletic when their contracts expire this summer.