Brinkley, 30, is a former fifth-round pick of the Vikings. He spent the first five years of his career in Minnesota before he signed on with the Cardinals as a free back in March of 2013.
The Cowboys elected to sign him to a two-year, $6.5 million contract that included $2 million guaranteed back in March. He was set to make a base salary of $1 million for the 2015 season.
Last year, Brinkley appeared in all 16 games for the Vikings in 2014 and recorded 75 tackles, one sack and a forced fumble. Pro Football Focus has him rated as the No. 16 inside linebacker out of 60 qualifying players.