Dusty Rose Levine arrived on Wednesday 21st September, a representative for the family confirmed to PEOPLE magazine, although the proud parents have not yet released any further details about their daughter, or shared any photographs.
Adam and Behati revealed that they were expecting back in March of this year, and a month later, confirmed that they knew the sex of the baby.
Adam could barely contain his joy about his daughter's impending arrival, saying to Entertainment Tonight's Sammy Hagar in August: 'I’m going to be a f***ing dad! I’m so excited! They let me make a baby! They let me make a baby!'
The pair have been keeping their fans updated on the progress of the pregnancy with plenty of social media snaps, with both taking to Instagram several times to share bump updates.
Around halfway through the pregnancy, Adam, 37, jumped on the bump photo bandwagon himself, uploading a funny picture of himself and his wife with the caption 'Week 20 and I'm finally popping! #impregnanttoo'
Adam, now 37, met Behati, now 27, back in 2012, and they dated for two years before tying the knot in a romantic ceremony in Mexico. At the time, Adam said he was ready to settle down, telling PEOPLE magazine: 'I definitely feel like I'm sitting in the chair I'm supposed to be sitting in right now. It all feels very natural.'
Neither member of the couple made any secret of the fact that they hoped to have children.
Speaking before Dusty's arrival back in 2014, Adam joked in an interview with Ryan Seacrest: 'I want to have 100 kids. I want to have more kids than is socially responsible' - so perhaps Dusty can expect some brothers and sisters in the future!