The footage emerged earlier on Tuesday and within hours police said three people, two men aged 20 and 18 and a boy aged 16, have been arrested on suspicion of affray.
They are now in custody for questioning, Greater Manchester Police (GMP) said.
Footage shows one youth telling the victim: “Don’t chat shit when you’re not even from England, you little f****** immigrant. Get off the f****** tram now. Get back to Africa.”
One of the youths, who all appear to be holding bottles of beer, then approaches and flicks alcohol from the bottle at his victim.
As the youths get off, the victim says to himself: “Seven years in the military”, as other commuters tell the three:”You are an absolute disgrace. A disgrace to England”.
The youths walk away shouting: “Salford! F****** immigrant!”
Chief Inspector Gareth Parkin from GMP said: “I would like to thank the public for their help and support in this investigation, which has led to the swift arrest of these three people.
“All hate incidents are treated with the upmost severity and this behaviour will not be tolerated in Greater Manchester.”
Greater Manchester’s mayor and police and crime commissioner Tony Lloyd said: “People across Greater Manchester will condemn racist attacks which have been reported in different parts of the country in the wake of the EU referendum result.
“While Greater Manchester Police have said they have not seen an increase in reports of hate crime over the weekend, we are now starting to hear stories of people being abused because of their race, religion or nationality.
“There is no room in Greater Manchester for hatred and division. We have worked hard, together, to build strong, cohesive, and welcoming communities. I encourage anyone who has been a victim of hate crime to come forward and report it.
“Hate crime has no place in our society. The overwhelming majority of British people stand together against hatred and prejudice. These acts of racism are not in our name and will not be tolerated.”
Anyone with information on the incident or other hate crime is asked to call to police immediately on 101 or the independent charity Crimestoppers anonymously on 0800 555 111.