I would not recommend round up or any other de-foliant chemicals. They can damage the soil. In some recent tests, the effects can linger for up to 7 years!
The best way, I have found in my lawn care and landscape business is to cut a one foot section out of the vines with a weedeater or some such device. Cut around the two foor mark from the base of your home. Then you can either let the ivy die, which takes quite some time, or begin pulling it off.
Grab the remaining two feet at the bottom and start pulling it back to exposes the roots. Cut them off as deep as possible, and just roll it up like a blanket. Keep going till its all removed.
I then like to dig out an additional foot or so and remove any excess that is there. Back fill the hole with good topsoil and start your landscaping.
Whatever you do, dont put the ivy in a composte pile. It just breeds trouble.