The actor, who plays bad boy Simon Barlow on the soap, and high school girlfriend Levi Selby, also 17, welcomed the child on Sunday.
Alex became a dad just a week after his 17th birthday, with his girlfriend sharing a picture of the tot with two love-heart emojis today.
The pair, who sat their GCSEs this year, were flooded with messages from well-wishers on Sunday after the birth of Lydia-Rose Bain.
Levi’s mum Judith Calvert posted on social media: “All I can say is my girl did herself proud.”
In May, The Sun revealed they were expecting a child after Alex proudly spread the news at his school in Lancashire.
The pair started dating in April last year and were said to have split in July. But Alex denied the rumours after Levi posted her 12-week scan on Facebook.
Alex said: “I’m still with my girlfriend, and can’t wait to have my own little family!”
Levi was targeted online by vile trolls after announcing the baby news, with one branding her a “slapper”.
But her mum rushed to her defence, posting: “Do not judge my daughter by your own low standards.”
A source said: “They’d had to deal with a lot and they’re both so young.
"But they’re absolutely over the moon – it’s the greatest gift they could have hoped for this Christmas.”
Alex’s portrayal of Ken Barlow’s grandson Simon saw him win Best Young Performance at the British Soap Awards in 2011.
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