Where/how did the military term, "Roger that", originate?

"Roger" was "phonetic" for "R" (received and understood". In radio communication, a "spelling alphabet" (often mistakenly called a "phonetic alphabet) is used to avoid confusion between similarly sounding letters. In the previously used US spelling alphabet, R was Roger, which in radio voice procedure means "Received". While in the current spelling alphabet (NATO), R is now Romeo, Roger has remained the response meaning "received" in radio voice procedure. In the US military, it is common to reply to another's assertion with "Roger that", meaning: "I agree".

- Major David Null, Auxiliary USAF, Claremont, CA USA

http://www.guardian.co.uk/notesandqueries/query/0,,-189587,00.html

masc. proper name, from O.Fr. Rogier, from O.H.G. Hrotger, lit. "famous with the spear," from hruod- "fame, glory" + ger "spear." As a generic name for "a person," attested from 1631. Slang meaning "penis" was popular c.1650-c.1870; hence the slang verb sense of "to copulate with (a woman)," attested from 1711. The use of the word in radio communication to mean "yes, I understand" is attested from 1941, from the U.S. military phonetic alphabet word for the letter -R-, in this case an abbreviation for "received." Said to have been used by the R.A.F. since 1938. The Jolly Roger pirate flag is first attested 1723, of unknown origin; jolly here has its otherwise obs. M.E. sense "high-hearted, gallant."

http://www.etymonline.com/index.php?term=Roger

the FBI/CIA dramas, the latest spawn of the TV police show fad. "Roger" is, as you've said, a radio code word used by police and similarly serious folk (at least on TV and in movies) to indicate that a message has been received and understood. The actual radio codes used by police forces vary considerably from place to place. In New York City, for instance, "10-4" (spoken as "ten four") has long been used as an acknowledgment, the equivalent of "roger," but in much of Ohio, a "10-4" or "Code Four" is a traffic accident. My local sheriff's department uses "You're clear" to indicate understanding, while in many other places "You're clear" would mean that an officer has permission to leave a scene and resume patrol.

There is, as you probably suspect, no person named "Roger" in this story. "Roger" is simply the word once used to indicate the letter "R" (for "received") in a particular radio alphabet, one in use during World War II but now obsolete. Radio alphabets are designed to unambiguously convey letters no matter how bad the reception may be. The current such alphabet, used by the US Armed Forces as well as civilian pilots, is the NATO Phonetic Alphabet, in which the letters are rendered as Alpha, Bravo, Charlie, Delta, Echo, Foxtrot, Golf, Hotel, India, Juliet, Kilo, Lima (pronounced LEE-ma), Mike, November, Oscar, Papa, Quebec, Romeo, Sierra, Tango, Uniform, Victor, Whiskey, X-ray, Yankee and Zulu.

"Roger" sounds a bit moth-eaten to my ears today, more associated with 1950s science fiction movies than CIA dramas, but it is still listed (and apparently used) by the US Air Force as an "operational brevity" word for acknowledging an order. They even still list "wilco" (short for "will comply)," although, mercifully, "over and out" seems to be passe.

http://www.word-detective.com/111606C.html#roger

The word is definitely the proper name, but it’s not been chosen randomly. Nor was there a famous early radio operator named Roger, as some wit somewhere is probably at this moment trying to convince somebody. It all goes back to phonetic radio alphabets, designed to transmit words by spelling them out letter by letter over poor-quality circuits. The phonetic expressions are chosen to be as distinctive as possible to limit the risk of confusing them.

We’re so used to the internationally accepted Alpha, Bravo, Charlie ... X-Ray, Yankee, Zulu alphabet, dating from about 1955, that only the older among us remember that there were others that preceded it. In particular, the phonetic alphabets used by the US Navy and the Royal Air Force from about 1941 both used Roger as the standard abbreviation for the letter R. Some at different times used the very similar Robert, but we are most familiar with Roger because it was standard for a large part of the Second World War.

The letter R, expanded to Roger, was used to mean message received, and had been in use in that sense ever since the early days of Morse code. Since the operator was often acknowledging receipt of a message on which he would have to act in some way, the response came not only to mean that he had received it, but that he had understood it, a subtle but crucial extension. (If he wanted to say explicitly that he would carry out an instruction, he would add wilco, short for “I will comply”. Hence all these handle-bar moustached aviators in films like The Dam Busters shouting “Roger, Wilco!” into their handsets before peeling off to do some deed of daring.)

This meaning for Roger became so stereotyped that it survived the shift to the international phonetic alphabet that almost everybody now uses, which instead has Romeo for R. It’s a good thing it only came in after the War: “Romeo, Wilco!” doesn’t have the same ring ...

http://www.worldwidewords.org/qa/qa-rog1.htm

the TROLL got it right:)