Bryan Keith Terrell, 47, accepted a final prayer but refused to record a final statement, the Georgia Department of Corrections said in a statement.
Terrell was convicted of the 1992 murder of John Watson, a friend of Terrell's mother, the Atlanta Journal Constitution newspaper said.
Terrell stole the man's checkbook and withdrew USD 8,700 from his account.
Watson told Ferrell's mother, Barbara, he would not press charges against her son if a substantial amount of the money was returned within two days.
Terrell's lawyers had pleaded for clemency.
They said they were concerned about the pharmacist who prepared the lethal execution drug, saying he had a shoddy record, and that the state should at least use a different pharmacist.