The newborn, whom Port named Sonny Sanford, was born on July 27, she wrote.
This is the first child for Port and her husband, Tim Rosenman.
"Everyone is so happy and healthy and we are home now. I'm going to try my very best to not be one of those moms whose feed is dominated by their baby but I can totally see how difficult it will be not to," she wrote. "I am beyond obsessed and in love and wish I could bottle this feeling for all of you out there."
Port, 32, announced this past February that she and her husband were expecting. The two were married in 2015, about three years after they went public with their relationship.