The song is considered by many as the Black national anthem and would precede the traditional performance of "The Star-Spangled Banner", the official US national anthem.
"Lift Every Voice and Sing" will be played or performed live before every Week 1 NFL game, as the league considers ways to recognize victims of systemic racism.
Goodell condemned racism and affirmed that Black lives matter, pledging his allegiance to the players in the battle for equal justice under the law.
Cruz wondered in a tweet whether there were national anthems for other races.
The NFL also may produce educational programs about victims, among other plans.
"We, the National Football League, condemn racism and systematic oppression of Black people", he continued. "[We] admit we were wrong for not listening to National Football League players earlier and encourage all to speak out and peacefully protest".
The league has been in discussions on the subject with the National Football League Players Association. "I personally protest with you and want to be part of the much-needed change in this country".
These measures come after NFL commissioner Roger Goodell seemed to signal a shift in how the league acknowledged such things when he said the league was wrong for not listening to past player protests. This will begin with the nationally televised first game of the season, which is on September 10, when the defending Super Bowl champions, the Kansas City Chiefs, host the Houston Texans. Both outlets further reported that the names of victims of police brutality will be displayed on players' helmets and jerseys.