A 41-year-old man has appeared before Melbourne Magistrates' Court charged with the rape and murder of Irishwoman Jill Meagher.

Adrian Bailey, from the suburb of Coburg in Melbourne, will now face a committal hearing on 18 January next.

The man was arrested following an investigation that began when the 29-year-old, who was originally from Co Louth, failed to return home after a night out with workmates in Brunswick.

Her body was discovered yesterday in a shallow grave at the side of a dirt road about 50km north-west of Melbourne.

Outside the court, Jill's husband Tom Meagher spoke briefly and thanked the public for the support he had received.

He also asked the media to respect the privacy of the Meagher and McKeon families.

Statement from Jill Meagher's family

Mrs Meagher's uncle Michael McKeon said: "We are devastated. We are heartbroken. She was the first grandchild my mother had and her aunts, uncles and cousins are powerless to describe their loss.

"There are no words to describe how we feel at what has happened. We had hope yesterday when there was no evidence of foul play but when the man in the CCTV footage was arrested we feared the worst."

Mr McKeon added: "We acknowledge the role that social media has played in the search for her. We believe that it has helped us to reach a conclusion although it is not the one we had hoped and prayed for.

"We thank the people around the world who have supported us."

"Both the McKeon family and Meagher family will have to plan now to grieve for Jillian and this is going to be one of the hardest things given that only three years ago we came together for the marriage of this lovely couple."