Does a Governor have the authority to deploy National Guard soldiers to another US State?

SSG Edward Tilton - The National Guard gets deployed to other countries all the time, every single brigade combat team of the Army National Guard has deployed in support of the GWOT to Iraq or Afghanistan or both multiple times. I just got back from a short stint overseas and I'm in the Guard. National Guard infantry, MP, and aviation units seem to be on constant rotation and it's regularly announced in the news that the Guard both Army and Air Force deploys. The Guard has contributed significantly to the fight overseas since World War I and will continue to do so.

SGT (Join to see) - They do it every time there's a request from another State because of a natural disaster or civil unrest which is common enough, especially in States like California that have wild fires every year or when a hurricane makes landfall like Harvey did in Texas.

In both of those instances multiple National Guard units provided support from multiple States.

LCpl Benji Smith - Some of it is just Active Duty stupidity or bravado, big Army doesn't always like to admit that the Army is made up of three components and it's not like they're educated on what the National Guard actually is. Some Soldiers knowing anything outside of their MOS would fry their brain. That said, I've met more than a few while overseas that had a lot of questions on how the Guard functions after the initial jokes as they had never worked with Guardsmen or Reservists prior to that.

SPC (Join to see) - In reality, the National Guard were some of the first units in Combat in WWI, WWII and Korea. Johnson's decision not to declare a state of emergency during Vietnam meant that the National Guard were not called up on a large scale basis during the conflict, even though individual Army National Guard units did serve in Country. The repercussions of that decision lasted through Desert Storm, where Guard and Support units from the Army Guard and Reserve were called up, but the Round Out Brigades were left stateside. You can blame Norman for that one.
The force makeup today is such that the Army can no longer function in a large scale operation without it's reserve components, which is the way it was always supposed to work.
The Air Force has always been better at integrating it's National Guard and Reserve assets than the Army. As an example, if you fly on military transport, the chances are pretty good that you are flying with a National Guard or Air Force Reserve crew.
I commanded a National Guard Divisional Engineer Company during Desert Storm, Divisional meaning that we were a Mechanized Sapper unit assigned to a Mechanized Division. We were trained and well equipped. We sat in Kentucky with our bags packed while they moved a Corp Level Engineer unit out of Europe to do that job, which is not how they were trained. I did a Keep Up tour with part of the Brigade a year or so after Desert Storm. The Battalion Officers were shocked when I told them that my operators, mechanics and drivers would have ran rings around what I saw in Germany. Had we deployed, it would not of been a problem to bring our squads up to the level of the Active Duty side. At Battalion level, I didn't see anything that scared me, I had been doing it for at least three years by that time.