Jessica also shared a personal photo to Instagram of herself with her newborn son sleeping gently on her arm.
"I couldn't be more in love with this squishy little man and his doting dad," she wrote.
Well wishes have poured in, including from some of Tim's Neighbours co-stars.
Scott McGregor wrote on Instagram: "Congratulations, guys!"
Olympia Valance added: "Oh my goodness!! Congratulations"
Tim rose to fame back in 2014 when he signed on to play Daniel Robinson — the son of Scott (Jason Donovan) and Charlene (Kylie Minogue) — in the popular soap series.
In 2016, after two years on set, Tim was written out of the series and left Neighbours.