According to OverTheCap.com, releasing these two players will free up $975,000 in available cap space while creating no dead money.
Howard, 26, originally signed on with the Texans as an undrafted free agent out of Ohio State back in 2013. He lasted just a few months with the Texans before later catching on with the Patriots and Giants.
The Falcons wound up signing Howard to a contract during the preseason last year.
He has yet to appear in an NFL game.
Mooney, 29, orginally signed on with the Titans as an undrafted free agent out of Army back in May of 2012. He spent three years in Tennessee before joining the Falcons in May of last year.
In 2013, Mooney appeared in 12 games for the Titans and caught six passes for 32 yards receiving and no touchdowns.