Burbidge and Knestout quoted Pope Francis saying that the death penalty is "an offence to the inviolability of life and to the dignity of the human person."
They added that "we have other ways to provide punishments and protect society, without resorting to executions."
"We too have been consistently clear in our stand on the abolition legislation this year and on similar legislation in years past, and in our direct interventions before executions occurred in Virginia and at the federal level," said the bishops.
The bill will now go to Gov. Ralph Northam (D) for signature. When the bill was introduced in the legislature on Jan. 13, Northam indicated that he would sign it into law.
The state Senate passed a bill repealing the death penalty on Wednesday, by a vote of 21-17. The bill passed by a party-line vote, as no Republicans voted for it and one abstained.
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The senate bill's sponsor cited concerns that the death penalty is disproportionately used against racial minorities and persons with diminished mental capacity.