The process is pretty straightforward and I did the same when I moved my LLC from Ohio to Texas. You basically form the the new Corporation and merge the LLC into it via an Asset Sale Agreement.
I retained the services of a local attorney in Texas to help draft the Asset Sale Agreement. The agreement details the transfer of the Name, EIN, "books", assets, intellectual property, goodwill, and liabilities et al. In my case, the purchase price was $10 as it is an IT Consulting Practice and there are no tangible assets. My agreement laid out 25 clauses in all and I signed as the seller and buyer.
Upon the merger, you follow the State of New York process to dissolve the LLC. In my case, I had to send the IRS a change of address form since I moved States. I kept the same name and no other action was required with the IRS.
In all, it was only a couple hours of an attorney's time and worth the investment. This is especially true if you plan to get third-party financing as it will prove chain of Intellectual Property ownership etc.