He has received education sessions “as part of the restorative justice process” following the incident.
Police say he backed their approach, which involved the use of anti-discrimination charity Kick It Out.
The boy was arrested after Wilfried Zaha revealed the messages before a defeat at Aston Villa in July.
A West Midlands police spokesperson told BBC Sport: “The boy was extremely remorseful for his actions and has received education sessions as part of the restorative justice process.
“This was victim-supported and led by Kick It Out.
“The sessions provided a greater understanding of equality, diversity, discrimination, and what is unacceptable behavior.
“They also highlighted the impact of hate crime on others and further punishments if he re-offends. We continue to work with the boy and there has been no repeat offending since.”
Zaha thanked fans in July for their “love and support”.
“People need to understand that whatever your age, your behavior and your words come with consequences and you cannot hide behind social media,” he said.
“It is important that social media companies do as they did and seek out these individuals and remove them.”