It follows the departure of Samantha Armytage to the weekday Sunrise edition last year.
Wright has reported for the show since its inception has been a fill-in presenter on the show for some time.
“Andrew and the team are some of the best people I’ve ever worked with in my 18 years at Channel Seven,” she said. “It is a unique show and I am truly honoured to have been offered the role.
“If you have to work weekends, to be able to do it with people you genuinely like and care about is such a bonus.”
“When it comes to storytelling, Monique is as good as it gets,” says executive producer Michael Pell. “She’s a terrific journalist and a great person. I have no doubt she’ll do wonderful things on Weekend Sunrise.
“Seven has a proud history of identifying and developing talent from within. Monique has been part of the Sunrise family from day one and this is the perfect next step in her already stellar career.”
Wright joined Seven in 1996 and has covered politics, human interest stories, celeb interviews, royal weddings and Olympic Games, including for Sunday Night.
She also continues as one of the four co-hosts of afternoon chat show The Daily Edition.