Dannii Minogue and Kris Smith met in Ibiza
Rumours of a split - fuelled by Tweets by them both - blamed Dannii's frantic work schedule for tension between the couple.
But Dannii, 39, and Kris, 32, say in a joint statement:
'Thanks for your concern. We're happy to be back at home in Melbourne together as a family. We are committed to our relationship and [son] Ethan as always.'
Dannii has left The X Factor but is a judge on Australia's Got Talent, runs her own fashion line Project D and has new book My Style to promote.
'We've now done two days of photo shoots for the book and I was so excited about some of the pictures that I got them to print me copies then and there so I can take them to show everyone when I get home to Melbourne next week,' Dannii wrote on her MyDaily.co.uk blog last week.
Kris, 32, was believed to be working in Manchester but arrived in Australia on Friday.
'Kris is not happy about Dannii's heavy workload, and wants her to spend more time with him and baby Ethan, and has put his foot down,' a source told the News Of The World.
Dannii and Kris met in Ibiza three years ago and their son Ethan was born last July.
Read about Dannii Minogue's exit from The X Factor in Now magazine dated 30 May 2011 - out now!