Hi Tracy,
The Seed Site has a pic of the berries being black, so I would wait until they change color to harvest. How long that will take, I don't know. I've never grown Jasmine, but I didn't want you waiting on an answer too long. Some seed pods ripen quickly, others take awhile.
Remy

Here is a link that might be useful: Jasmine Berries and Seeds on The Seed Site

What a great seed website, Remy! :) However, I beg to differ re. the seeds, as the plant with white berries sounds very much like cestrum nocturnum... the common name is night blooming jasmine, but of course common names can be misleading or shared by a number of plants. I have a cestrum nocturnum and the berries stay white and turn a spotty tan as they age. I would guess that a ripe berry is spotted with tan or is entirely tan and wrinkly a bit. Hope this helps a bit! :)

Thanks nuitjasmine. You're right common names can be confusing.
Remy

I have heard alot of people say they move there night blooming jasmine in and out of the house. After a while is the plant not strong enough to stay outside, if it is well taken care of.

Cestrum nocturnum also known as Night Blooming Jasmine, is grown in subtropical regions as an ornamental plant for its strongly-scented flowers. It grows best in average to moist soil that is light and sandy, with a neutral pH of 6.6 to 7.5, and is hardy to hardiness zone 8. Feed bi-weekly with a weak dilution of seaweed and fish emulsion fertilizer.

All parts of the plant are highly poisonous.
Just picked this up off a website.