Prosecutors had asked Warner to grant the pardons after he exonerated both men last week. Both had previously been paroled after serving long prison sentences.
Three other men have also been cleared by evidence saved by the late Mary Jane Burton. A review by an independent lab of all samples saved by Burton has been ordered.
Thurman was convicted in 1985 of rape, abduction and assault. According to the state Corrections Department, he was sentenced to 31 years in prison and was paroled in February.
Davidson was convicted in 1981 of sexual assault. He was paroled in 1992 after serving more than 11 years in prison.
Authorities said both men were convicted based on witness identifications.
Warner said last week that the review of evidence in Thurman's case resulted in a match in the state DNA data bank, but no charges have been filed.
Burton, who died in 1999, worked in the state crime lab from 1974 to 1988 and habitually saved pieces of the evidence she handled — even before DNA testing had been invented.
Over the years, she inserted into case files such things as cotton swabs and clothing fragments smeared with blood, semen and saliva. The files eventually landed in a storage facility.
The samples were forgotten until 2001 when the head of the state Department of Forensic Science discovered a case file with an old cotton swab.