The song's lyrics include the lines: "Mr Watson, I've been cheating with you / You're the only one to fix the stupid s*** I've been through."
The video is a big step back into the public domain after Kills and Moon's outburst on The X Factor NZ against contestant Willy Moon made worldwide headlines and saw the pair sacked as judges.
On Twitter, Kills - who has changed her name to Teddy Sinclair - said she got straight back into songwriting after The X Factor outcry died down, contributing songs to recent albums by Madonna and Rihanna.
She also called the X Factor incident a "publicity stunt resulting in a viral media storm".
"I was subjected to a global witch hunt I couldn't defend myself against due to a wide-reaching legal gagging order," she wrote in February.
During a live broadcast, the pair accused Irvine of ripping off Moon's image. Moon was particularly savage, wondering if Irvine might "stitch someone's skin to your face and kill everyone in the audience".
Irvine recently told the Herald he can't watch repeats of the incident and wrote a song about it called Addiction that helped aid in his recovery.
"The track is about where Natalia Kills is at now and the highs and lows I went through because of her," he told the Herald on Sunday. "I wish her and Willy well. I just hope they never do anything so stupid and uncalled for again."
Read more: Joe Irvine says he's still traumatised by Natalia Kills, Willy Moon
Sinclair and Moon have been hyping up the video launch for Mr Watson through their social media accounts.
