Cole, who was serving a 25-year sentence, died in prison in 1999. After DNA testing, Cole was exonerated by a Travis County judge in 2009.
He was serving time for the rape of a Texas Tech student in 1985, a crime he did not commit.
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Another man, Jerry Wayne Johnson, sent a letter to Cole's mother confessing to the crime.
Governor Perry signed the pardon papers in on March 1.
On Friday, Cole's mother, Ruby Sessions, plus his brothers and sisters attended a ceremony where the Governor presented the pardon document and a flag which flew over the state Capitol.
"Words can't describe it, I just said that I asked them for three years for that little piece of paper," said Ruby Session, Cole's mother. "But I didn't realize it was gonna be framed and mounted, but I have that little piece of paper, and this is a glorious day."