Marcus Rashford, Bukayo Saka and Jadon Sancho were targeted after they missed penalties in the Euro 2020 final.
Chief Constable Mark Roberts said the abuse was “utterly vile”.
“If we identify that you are behind this crime, we will track you down and you will face the serious consequences of your shameful actions,” he said.
Police said “a torrent of racist comments aimed at some of the team’s black players” appeared on social media platforms on Sunday, after England lost on penalties to Italy in the final at Wembley.
The UK Football Policing Unit said its team was working through “a significant number of reports of racist abuse”.
Local police forces had made the four arrests, a statement said.
Chief Constable Mark Roberts, National Police Chiefs’ Council football policing lead, said the racial abuse “has quite rightly shocked and appalled people across the country”.
“Our England team have been true role models during the tournament, conducting themselves with professionalism and dignity. I’m disgusted there are individuals out there who think it’s acceptable to direct such abhorrent abuse at them, or at anybody else.”
He said the investigation would continue to try to find those responsible and officers were working closely with social media platforms, including Facebook, Instagram and Twitter.
England manager Gareth Southgate has said the racist abuse aimed at Rashford, Sancho and Saka was “unforgivable”.
And Prime Minister Boris Johnson has promised to ban people guilty of sending racist abuse to footballers from attending matches.
He said he would ensure the “football banning order regime is changed” to crack down on racism.
The UK Football Policing Unit said, as of 13 July, 897 football-related incidents and 264 arrests had been recorded across the country in the 24-hour period surrounding the final.