The Candy singer has written six new tunes with Chambers, who has also produced the album.
Speaking of the record, Williams said: "First of all, I wanted to do a swing album because I wanted to do a swing album.
"I always knew I'd do another and I think now is the perfect time to do it. I'm enjoying showbiz and I'm enjoying my life and my understanding of where I am now is that there needs to be an event every time I bring out a record."
He continued: "The album this time is a definite ode and a loving glance towards a period on the planet that I was never invited to 'coz I wasn't there… I wanted to be, which I feel still very strongly linked to.
"Going in I planned it to be very similar to the last one, and then I realised – that's actually not what I wanted. It's different – it's not all covers.
"I had some songs that I wanted the world to hear and check out and maybe become part of the fabric of their lives, if I'm lucky enough, that I've had a hand in writing."
Robbie added: "So it's very, very similar to the last one, and very different – and hopefully I'm off to romance the world!"
Williams first swing LP, Swing When You're Winning, has been certified seven times platinum since its release in 2001, and is his best-selling record to date.