Evidently, Williams is signing with the Nets for the equivalent of the "room/stretch exception": 2 years, $5 million. It's hard not to think that Williams was a little bit put-off when the Knicks prioritized trying to sign Jamal Crawford over him, but the lure of a starting spot probably helped seal the deal too.
In the meantime, the Knicks will turn their attention to some other possibilities to add to the bench. Some names I've heard thrown around are Maurice Evans, Michael Redd, Bostjan Nachbar (who worked out for the Knicks a few weeks ago), or possibly Travis Outlaw if New Jersey uses the amnesty clause on him. If Baron Davis clears waivers, he is very much on the Knicks' radar.
In the meantime, good luck in New Jersey, Shawne! We appreciated a year of your services.