The deal is worth a little more than $4 million, according to sources.
Parnell, who was the swing tackle in 2011 and saw limited action in six games, will receive a $1 million signing bonus.
The Cowboys tendered him a deal as an exclusive-rights free agent earlier this offseason, so in essence they bought out his restricted free-agent year and his first year as an unrestricted free agent (2014).
Dallas added Parnell, a former basketball player at Ole Miss, off the New Orleans Saints' practice squad in 2010. He was inactive for 12 games in 2010.
The Cowboys have Tyron Smith as their starting tackle but did not have a veteran presence at the position. The Cowboys are high on Parnell's potential because of his athleticism.