The 41-year-old captioned the fun picture of Axl: "babies, start your engines!"
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Axl's turn as a Formula One driver follows the adorable snap Fergie posted last week to celebrate Josh's birthday.
"HAPPY BIRTHDAY DADDY!!!!" wrote the Black Eyed Peas singer alongside the photo on Twitter, which featured the cute baby beaming at the camera.
Josh and Fergie are loving being first-time parents. "First of all, we're obsessed with him," Josh told E!. "We can't stop staring at him. He's our little man, we made him together."
"I think there's something you can't really describe until you go through it," he added. "I think any parents out there would understand that. It's just an incredible time for both of us."
Axl made his enterance via scheduled C-section on 29 August and weighed in at 7 pounds and 10 ounces.
It is thought that the baby's unsual name has been inspired by Guns N' Roses rocker Axl Rose.
The new mum, 38, is a big fan of the band and even performed Sweet Child O' Mine with guitarist Slash during the Black Eyed Peas' Super Bowl halftime show in 2011.