Brookshier had 20 interceptions in seven seasons with the Eagles, earning All-Pro honors in 1959 and 1960, before a compound fracture in his leg ended his career in 1961.
"He was a hitter," Bednarik said in a statement released by the team. "We've lost one of the great Eagles of all time."
Brookshier was a 10th-round draft pick out of Colorado, and he had eight interceptions as a rookie in 1953. That's still tied with Bibbles Bawel for the Eagles' single-season interception record.
Brookshier served a two-year stint in the Air Force before returning to the NFL in 1956.
"Nobody said we were going to beat Green Bay," McDonald said Saturday. "Well, look at what we did! The 1960 team lost a brother. That 1960 team was family. He had an outstanding personality. He was a happy person to be around."
Even years later, Brookshier remained a revered figure in Philadelphia.
Brookshier is one of seven Eagles to have his number retired, and he was inducted into the team's Honor Roll in 1989. After he retired from football, Brookshier announced NFL games with Pat Summerall for CBS.
"Tom Brookshier will be missed by his friends, colleagues and admirers," CBS Sports president Sean McManus said in a statement. "His voice and his style will forever be part of the history of sports television and proudly recognized in the foundation and the future of CBS Sports."
The Associated Press contributed to this report.