The Moneyball actor - who also raises Pax, 9, Zahara, 7, Shiloh, 6, and 4-year-old twins Knox and Vivienne with fiancée Angelina Jolie - purchased a Suzuki DRZ-125 for Maddox, and has had a motocross trail built in the grounds of their French estate.
A source told The Sun: "Brad's always been a generous dad and as Maddox has shown a keen interest in bikes, he thought he may as well get him started.
"He was down at the house the other week and got the builders to dig him a muddy trail all through the woods and around the lake.
"Brad was just as excited as Maddox about it, though - he's put in little jumps and puddles so they'll get really muddy.
"The bike has an automatic clutch and, of course, Brad's bought him his own helmet and protective gear.
"Brad took him into the garage and there the bike was with a bow on it. Maddox was over the moon and couldn't wait to try it out. He was riding it around all day at the house, tearing up the lawn."
Watch a clip of Brad Pitt's latest film Killing Them Softly below: