Mr Woods was convicted in 2005 of the shooting of three police officers, but his co-defendant Kerry Spencer later claimed he was not involved in the shooting.
In a letter from death row where he is also held, Mr Spencer wrote that Mr Woods is "100% innocent" and asked for the execution to be stopped.
Celebrities joined Mr Spencer in trying to halt the execution, with Martin Luther King III and reality star Kim Kardashian-West tweeting their support for Mr Woods.
Kardashian-West urged her followers to contact the state governor and called the execution tragic.
Below is all you need to know about the death penalty in the US.
Which states still have the death penalty?
25 states, including, Kansas, Indiana, Virginia and Texas still have the death penalty, with the law in force in areas all over the country.
Four others, Colorado, Pennsylvania, California and neighbouring state Oregon have Governor imposed moratorium, which is a suspension of a law until deemed worthy again.
Do they all use lethal injection?
Lethal injection is the primary method of execution in all states that have the option of the death penalty.
Secondary methods are available in 16 states, including South Carolina, Tennessee and Oklahoma.
The most widely used secondary method is electrocution, followed by lethal gas.
In New Hampshire and Washington, hanging is a secondary method, with a firing squad available in Utah.
Is there any likelihood they'll stop any time soon?
33 states have either abolished or have not used the death penalty in the last 10 years.
Of the 25 states still with the law, 18 haven't executed anyone in the past five years and 12 haven't in the last 10.
Since 2007, nine states have abolished the death penalty, but four of those have Governor imposed moratorium.
In 2015 Nebraska abolished the death penalty, but reversed the decision a year later.
Texas has had the most executions since 1976 with 569, followed by Virginia on 112 and Oklahoma on 111.
There were nine executions in Texas in 2019 and the state has executed the most people every year since 2002.
More states are moving towards abolishing the death penalty, but as Nebraska's reversal and Texas' continued use shows the US is still a long way off abolishing it everywhere.
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