The final steps of the server move will take place at approximately 0300 UTC June 17th.
At this time the site will remain largely accessible except for the forum will be set to maintenance mode.
Shortly thereafter the site's domain name will be pointed towards the new server, and the forum will become useable again as the domain changes take effect. This could theoretically take up to 72 hours for some users but it is my experience that it usually takes more like 12 hours or less for most.