Johnson is expected to miss as many as three weeks if it becomes apparent that he'll have to have arthriscopic surgery.
DiNapoli agreed to a one-year deal that will pay him $530,000 and includes a signing bonus of $150,000.
DiNapoli, orginally a 4th round pick out of Virginia Tech in the 1998 NFL Draft, is a 6-year veteran who has spent the last three seasons with the Tennessee Titans. He was traded to Tennessee from the Oakland Raiders for a 7th round pick in 2000 draft.
DiNapoli is excited about coming to Valley Ranch.
"The Cowboys have a great tradition," DiNapoli told the Dallas Morning News. "It's like playing for the Yankees in baseball."
DiNapoli, who can play either guard or center, will probably not be ready to participate in the Cowboys first preseason game of the year against Arizona this weekend.
The former Virginia Tech Hokie started all 16 games at center last season.
Cowboys Add Another Center
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