Once a member always a member everywhere. You need to start talking to the new chapter as soon as you can so they know you're coming. They may have a process to affiliate. Some orgs it's automatic and some the chapter votes. Your national probably has something you're supposed to do to transfer your membership from one chapter to another, but that's probably not a big deal. Just talk to the guys and you'll figure it out. They are your brothers afterall.
This is true, but the OP shouldn't take it personally if they do not allow him to affiliate. Chapters can vary greatly and you might not fit into this one. When I went to our national convention, there were some chapters I know I wouldn't fit into and there were some people who I knew my chapter would have never given a bid to.