The schools announced the games Thursday night.
The teams will play at Texas A&M in 2018 and at Clemson in 2019.
The schools have played four times previously, the last coming in 2005 when the Tigers beat Texas A&M 25-24 at Clemson's Memorial Stadium.
The games mean that Clemson will face two Southeastern Conference schools each season from 2016 through 2019. Clemson plays Auburn in 2016 and 2017 before picking up Texas A&M. Clemson closes the season each year against state rival South Carolina.