You need a Pet Passport, from your vet. I would contact DEFRA, the UK regulating body to find out the regulations for the place you are moving to and whether you need to know anything special.
The procedure usually goes as follows here in the UK (I have sorted out a LOT of UK Pet Passports!), and I think the US in included in the scheme.
1) Your cat(s) must be microchipped & vaccinated for Rabies, as well as be up to date on booster vaccinations.. (UK pets are usually not vaccinated against rabies - the UK is rabies free!)
2) 4 weeks after the Rabies vaccination, your cat(s) goes back to the vet for a blood sample and microchip reading. The sample is sent off to an external lab to test for Rabies antibodies, and the microchip number is double checked and verified.
3) Once the blood test comes back with required antibodies, you are issued a Pet Passport Certificate. You can leave the UK to any of the countries on DEFRA's website. HOWEVER - you cannot return to the UK until 6 months after the Passport was issued, and the cat(s) must recieve yearly Rabies boosters and worming before coming back.
Contact your vet to sort out an appointment for the vaccs/chip.