CEO Kevin Johnson, in a statement, expressed the company's "deepest apologies" to the men for what he said was the "reprehensible outcome" of the incident.
Mr Johnson said the company would investigate and "make any necessary changes" to avoid a recurrence.
"Starbucks stands firmly against discrimination or racial profiling," he said.
The video posted by a Starbucks client shows several uniformed police officers questioning and then handcuffing the two men, who offer no resistance.
In the foreground, a white client objects to the scene, repeatedly asking an officer, "What'd they do? What'd they do?"
The woman who posted the video, Melissa DePino, tweeted: "The police were called because these men hadn't ordered anything. They were waiting for a friend to show up, who did as they were taken out in handcuffs ... All the other white (people) are wondering why it's never happened to us when we do the same thing."
She said it was a Starbucks employee who called police.
The two men's lawyer Lauren Wimmer said they were waiting for a third man to arrive for a business meeting.
Philadelphia police commissioner Richard Ross, who is black, said police had received a 911 call from a Starbucks worker who said the men were trespassing, after sitting down and refusing to buy anything.
Mr Ross said his men had "politely" asked the two to leave before finally arresting them.
The men were released after Starbucks declined to prosecute them.
Mr Johnson, in his statement, said the store manager never intended for the men to be arrested, adding that he hoped to meet them personally "to offer a face-to-face apology".
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