1 : to relieve of a responsibility, obligation, or hardship

2 : to clear from accusation or blame

Examples: 

Dana was exonerated for the crime of taking the money after it was found that her fingerprints did not match those on the cashbox.

“… a 2015 measure approved by the Legislature will provide more opportunities for convicted people to request DNA testing of evidence that might exonerate them.” — The Daily Herald(Everett, Washington), 23 Dec. 2015