The Strokes frontman ended his 15-year marriage to Juliet Joslin - the mother of his sons Cal, 10, and five-year-old Zephyr - last year and has now found love again with a younger tour worker named Kaya.
A source told The Sun newspaper's Bizarre column: "Julian split from Juliet about a year ago but has been determined to keep it private but now he's moved on he can't really pretend it hasn't happened any more."
The 41-year-old singer is said to be "inseparable" from Kaya, who is in her early 20s.
The insider added: "Him and Kaya have been getting really close for months and now they're pretty inseparable.
"He even takes her backstage with him at huge events such as gigs at the Barclays Center in New York.
"If the band goes somewhere for a tour or anything else, Kaya goes with him. His dad left his mum and got with a much younger girlfriend too."
A spokesperson for the 'This Is It' hitmaker confirmed Julian and Juliet had split "with love and respect" more than a year ago and insisted the former couple - who married in 2005 - still get on well for the sake of their sons.
The representative said: "With love and respect, Julian and Juliet chose to end their marriage over a year ago. They are happily raising their boys together.
"Out of respect for his family, he will not be discussing this aspect of his personal life any further."
Julian recently opened up about fatherhood and admitted he is keen to protect them from "intense darkness" but also for them to understand the real world.
Asked if nurturing comes naturally to him, he said: "I don't think I had that so much before kids. Probably the opposite.
"But it's a balance: You want to protect them from intense darkness that can damage them, but you want them to get their lumps and feel enough reality and emotional truth to be tough and ready for the real world."
