updated 05/02/2012 AT 9:00 AM ET
•originally published 05/02/2012 AT 10:05 AM ET
“Proud PaPaJoe !! Beautiful baby girl… What a miracle!” excited grandfather Joe Simpson Tweeted Tuesday.
Meanwhile, Jessica’s sister, Ashlee, told PEOPLE she’s already “in love” with her niece. “Jessica has wanted to be a mom since we were little girls and I couldn’t be more excited for her and Eric,” she said.
Fellow mom-to-be Nicole “Snooki” Polizzi also had words of encouragement.