Webber, 38, also took to Instagram to share the news, revealing the birth led him to get their daughter's name tattooed on his neck.
"I whispered her a poem as soon as she was born. Our beautiful baby girl Poet Lake Palmer has arrived,” he wrote. "We’re all in total bliss."
The happy couple— who met in 2012 and got engaged in August 2013—are also parents to Forest Sage, 2, and Bodhi Rain, 5. Webber is also dad to 10-year-old Isaac Love who he shares with ex-girlfriend Frankie Shaw.
Palmer announced she was pregnant in October of last year, sharing a photo that showed off her bulging baby bump.
“Thank you for all the beautiful messages 💛 we are overjoyed but mostly very grateful,” she captioned the post, adding that she was due in April.