The incident took place on October 25, 2018 at Almondbury Community School in Huddersfield.
A video of the assault of the 15-year-old Syrian refugee was shared extensively on social media.
In the footage, the victim is thrown to the ground and threatened with drowning.
It provoked outrage and prompted well-wishers to set up an online crowdfunding page for the victim which received £50,000 in donations in the space of a day.
The 16-year-old perpetrator has been given a police caution.
West Yorkshire Police said it had investigated whether a racially aggravated assault had taken place at Almondbury Community School in October last year.
On Thursday, the force said in statement: "The CPS (Crown Prosecution Service) has concluded that there was not sufficient evidence to charge the suspect with a racially aggravated assault and he was given a caution for a section 39 assault."
The police statement said: "Included in the report received by police, was the video evidence of the incident, which has been widely circulated in the media and on social media.
"The suspect was interviewed by police.
"Upon completion of the investigation, it was reviewed by the youth offending team, the suspect was reported for summons for section 39 assault.
"However, following significant media coverage about the incident, West Yorkshire Police has received further intelligence and evidence and a review of the case was undertaken to investigate whether there was a racially aggravated element to the offence."
The statement concluded: "The victim and his family has been kept updated throughout the process and has been updated on the CPS's decision."
Shortly after the footage emerged, the victim said he no longer felt safe at school.
He told ITV News: "I woke up at night and just started crying about this problem.
"They think I'm different - different from them.
"I don't feel safe at school.
"Sometimes I say to my dad, 'I don't want to go to school anymore'.
"I was just crying and I didn't do nothing because I respect the school rules."
Prime Minister Theresa May said the generous public response showed the "true spirit of Britain".
After the video was widely shared and the incident attracted massive media attention, the perpetrator gave The Sun Online a handwritten statement in which he accepted responsibility for his actions, but denied bullying the younger boy.
The teenager, who has not been named, said he and his family had gone into hiding after a video of the incident was widely shared online.
In an interview last year with English Defence League founder Tommy Robinson, a convicted fraudster whose real name is Stephen Yaxley-Lennon, he said he was "scared for my life, scared for my family's life".