Jon Gruden commissioned an impromptu Jon Gruden impression from Frank Caliendo at an Aerosmith concert recently ... and the video is laugh-out-loud funny.

FYI -- Caliendo has been doing an insane JG impression for YEARS ... and even famously did the bit for Gruden's Raiders at their training camp this past summer.

So, when Gruden was sitting next to the comedian in an arena waiting for the show to begin ... he whipped out his phone and created 25 seconds of magic with the guy.

JG starts the video by saying, "Yes, I'm sitting here at the Aerosmith concert with my good friend, Jon Gruden. How's it going, Jonny?!"

That's when Caliendo takes it away ... SOUNDING EXACTLY LIKE JON!!!

Frank, though, cracks up throughout the whole impression ... and his explanation for why is hilarious.

"1. Gruden recorded this on his phone," Frank said. "2. He didn’t tell me he was going to do it- and that's why I'm laughing so much. 3. I asked him to send it to me so I could post it. 4. He did... so that should tell you how great he is."