According to reports, the baby arrived around 5:30 a.m., at Matsu Regional Hospital in Wasilla, Alaska.
Breeze, whose curious middle name Beretta was inspired by the name of the Italian firearm manufacturer, came in at 6 lbs and measured 19 in.
The couple has been dating since 2010 and this is their first child together.
As RadarOnline.com previously reported, the child was conceived on a hunting trip when Oglesby, 20, forgot to take her birth control.
Since his relationship with Bristol fizzled, Johnston went on to pose for Playgirl magazine and recently wrote an autobiography titled Deer in Headlights.
There has been bad blood between he and the Palins since their 2010 break-up. Despite having not seen the child for more than a year at one point, Johnston has recently petitioned for full custody of Tripp.