His fiancée Sarah Jane Honeywell gave birth to a baby boy on Tuesday (August 25), but the couple have yet to announce the child's name.
He wrote this morning: "Back at hospital after our little man made his appearance last night 8:31pm. Mum and baby doing great, both beautiful."
"Changed a nappy that looked like he'd been out on the Guinness. Now just watching the both of them sleep. Best day ever," he added.
The couple announced their impending arrival in May, posting a picture of themselves at The Baby Show.
Callaghan is currently starring as Joe Roscoe on Hollyoaks. He previously played Miles De Souza on Emmerdale.
The actor's Hollyoaks co-stars - from James Sutton to Jessica Fox - have been tweeting their congratulations:
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@AydenCallaghan congratulations guys
— Gemma Merna (@gemmamerna) August 26, 2015
@AydenCallaghan ahhh congratulations you pair xxx
— Anna Passey (@MissPassey) August 26, 2015
@AydenCallaghan yes!! Congrats big bear!! All the love x
— James Sutton (@thejamessutton) August 26, 2015
@AydenCallaghan fantastic news!! Congratulations to you both xxxx
— Jessica Fox (@JesslaFox) August 26, 2015
@AydenCallaghan many congratulations to you both. Great news x
— Greg Wood (@gregwoodactor) August 26, 2015
@AydenCallaghan Oh what amazing news! Congratulations, we're so happy for you both.
— Hollyoaks (@Hollyoaks) August 26, 2015
