Waugh, best known for playing Cheryl Brady on the Channel 4 soap, has been cast as the wife of a serial killer in upcoming BBC thriller The Fall.
Richardson, who plays Chester's Ste Hay, has now told Digital Spy that he is thrilled over the success of his colleague and best friend.
He commented: "This is something I'm really excited about, because I think Bronagh Waugh is an amazing actress and she doesn't get the credit she deserves. She's never really nominated for 'Best Actress' or anything like that, because Cheryl is a very comedic character.
"So when I heard about the news that she was auditioning for this, in my head I was thinking, 'Wow - it's a really big part and I hope she gets it'. And then when she told me that she'd got the role, it was just amazing."
Details of Waugh's new part were officially announced yesterday. The 29-year-old is currently filming the programme in Belfast, juggling the five-part series with her Hollyoaks commitments.
Richardson added: "She's told me the plotline and I think the stuff that she's going to do is going to shock a lot of people! I think it will put Bronagh on the map, really."
The Fall, which also stars former X-Files actress Gillian Anderson, will air on BBC Two in September.