The 36-year-old's partner Stacey Gardner gave birth to a baby boy on April 29.
He took to Twitter to announce the arrival of baby Brandon.
On April 30, he posted: "My new born son, Brandon, arrived yest, 8lb 9oz, wee cracker!"
The baby arrived days after Harrison appeared at Glasgow's Justice of the Peace Court and was fined £800 for driving without a licence or insurance in Govanhill.
During the hearing his defence lawyer said Harrison was on benefits of £180 a fortnight.
The boxer is dad to three other children.