Nothing in the constitution lays out any requirements for the form or logic of a Presidential pardon, other than "I say so". So he said so on twitter. This is the only version that seems to have been released to the public in any sense directly from the White House or the government in general.
Thanks to the comments of Carpetsmoker and origimbo, it appears that Arpaio himself received a more formal and specific pardon, which has made its way into the public through media interviews.
Wikipedia image file
This image appears in a Washington Examiner article, and is attributed to a Twitter post of Michael Keiffer, who interviewed Arpaio. Assuming this is the actual pardon Arpaio received, the seal of the Department of Justice would indicate that some copy of the file is on record somewhere within that Department.
Arguably, the only restriction the constitution places on the president's pardon power is that it can only be used to pardon federal crimes. Current legal opposition to the Arpaio pardon is based less on "the constitution specifically says you can't do this" and more on the meta-argument of "what's the point of even having a constitution if he can do this kind of thing?". There are other Q&A's on this site that deal with this more specifically.
In fact, pardons can be very non-specific, so that rules-lawyering lawyers don't try to circumvent the intent with technicalities. The pardon of Arpaio is fairly specific, though the second point is non-specific: no specific crimes are pointed out, just completely arbitrary crimes that otherwise fall under a particular legal umbrella. At the extreme end, Ford's pardon of Nixon was for any and all crimes committed, possibly committed, or in any way involved in, over a period of several years.
do grant a full, free, and absolute pardon unto Richard Nixon for all offenses against the United States which he, Richard Nixon, has committed or may have committed or taken part in during the period from January 20, 1969 through August 9, 1974.