The deal is worth $6.87 million and includes a $3.37 million signing bonus, according to ESPNDallas.com.
Frederick was the 31st overall pick in April's NFL Draft, a pick where many experts thought the Cowboys reached. Frederick himself was surprised to be taken so high. "I thought somewhere in the second round would be more of a fit for me," Frederick said after the draft. "I truly didn't expect this."
The Cowboys went into the draft with the 18th overall pick but traded down with San Francisco to the 31st spot.
Frederick should be able to help right away.
The Cowboys are in dire need of some consistency at center after going through six players at the position last season. Frederick is the front-runner to be the team's starting center when the regular season opens in September, however, he will see some competition from Phil Costa, who's going into his fourth year with the Cowboys.
Costa started all 16 games in 2011 before being limited to only three games last season due to an ankle injury. Costa signed a two-year deal with the Cowboys in March.
With Frederick's signing, the Cowboys now have their entire 2013 draft class under contract.