Money for the programme will come from the city's finance department budget, Dunn said. The city, Nelson and Robinson will together develop a committee to award grants.
The city has also invited Robinson, Nelson and their lawyers to submit thoughts and recommendations to the city solicitor on other ways of promoting equality in public places, including restaurants and retail establishments.
When asked whether the grant will focus on helping young entrepreneurs of colour, Dunn said "we are still working out those details".
Cohen, Placitella and Roth, the Philadelphia law firm representing Nelson and Robinson, did not immediately return a request for comment.
Starbucks said it had reached an agreement with Nelson and Robinson that will include an undisclosed financial settlement "as well as continued listening and dialogue between the parties and specific action and opportunity".
Starbucks executive Kevin Johnson said he welcomed the chance to begin a relationship with Nelson and Robinson "to share learnings and experiences".
"Starbucks will continue to take actions to repair and reaffirm our values and vision for the kind of company we want to be," Johnson said.
A company news release said more details "will be provided in a mutually agreed public statement".
On April 12, Nelson and Robinson arrived 10 minutes early for a business meeting at a Starbucks in the Centre City neighbourhood of Philadelphia and wound up leaving the location in handcuffs. Upon arriving, Nelson asked whether he could use the toilet, and was told by a white manager that the restrooms were only for paying customers.
"And I just left it at that," Nelson told Good Morning America last month.
After Nelson returned to the table where Robinson was sitting, the manager approached them to ask whether she could help get them any drinks or water.
Two minutes later, she called the police to report that "two gentlemen in my cafe that are refusing to make a purchase or leave."
Officers arrived a few minutes later. Robinson recalled thinking "they can't be here for us".
Nelson told Good Morning America that the police told him and Robinson that they had to leave without any discussion. They were then arrested, and Robinson said they were not read any rights or told why they were being arrested.
Charges of trespassing and creating a disturbance were dropped that night.
Shortly after Nelson and Robinson told their story, Philadelphia Police Commissioner Richard Ross personally apologised and said that if he had done anything to worsen race relations in the city, "shame on me". Ross had previously said the officers involved "did absolutely nothing wrong".
Last month, Starbucks announced it would close 8000 stores for racial-bias training on May 29. Johnson, as well as the company's executive chairman, Howard Schultz, met Nelson and Robinson personally to apologise.
As protests broke out at the Philadelphia Starbucks, Johnson and Schultz appeared in television interviews to pledge that the company would work to combat unconscious bias and racial profiling among its employees.
In a video message, Johnson said, "I will fix this."
