Dudley Davey, 35, pleaded guilty to both the rape and murder of the 56-year-old, who was found buried in a shallow grave three days after she went missing from her home in Fregon, in SA's north, in March last year.
South Australian Supreme Court Justice Ann Vanstone jailed Davey for life on Thursday and set a non-parole period of 32 years.
"This was a cold-blooded killing of a woman who had worked with skill and compassion in your community," the judge told Davey.
“Dudley Davey should never ever be let out of jail for the shocking crime he committed."
Justice Vanstone said the drug addict and serial offender had chosen Mrs Woodford as an "easy target, vulnerable because of her empathy".
She said Davey's offending was "callous in the extreme" and at the higher end of the scale for the crimes of rape and murder.
Outside court, Mrs Woodford's husband Keith said he hoped Davey would never be paroled.
“Dudley Davey should never ever be let out of jail for the shocking crime he committed," Mr Woodford said.
"We will always mourn Gayle but so many people have helped us to cope with the tragedy of her death."
Elders don’t want killer to "return to country"
The sentence comes after Aboriginal elders told the South Australian Supreme Court that Davey will never be allowed back on to the APY Lands.
In a victim impact statement delivered on behalf of all people on the state's Anangu Pitjantjatjara Yankunytjatjara lands, Ms Woodford's death was described as one of the biggest losses suffered by the local community in living memory.
"A dark cloud covered Fregon since the day Gayle's body was discovered in a shallow grave," Elders said.
"Such dark cloud has cast a shadow since then. Only a few have found a glimmer of light."
Elders said Gayle was one of the warmest people to ever work in Fregon.
"Gayle was not scared of the Aboriginal people. She treated the able and the disabled, the frail and unwell, the educated and the uneducated, the employed and the unemployed, justly and fairly," Elders said.
"Gayle was a kind and dedicated nurse who truly nursed as nursing should be done.
Community leaders have also told the court that Davey, who has a long history of offending, would never be welcome in the APY lands again.
"He is not welcome, ever."
They said he should never be allowed to "return to country" upon his release from prison.
"He is not welcome, ever," they said.
Justice Vanstone said Davey had gone to Mrs Woodford's home in Fregon with the intention of enticing her outside so he could rape her and "that's what you did".
She said he then decided to kill her in the hope of covering up the rape and theft of the ambulance Mrs Woodford used in her work at the Fregon health clinic.
A post-mortem examination found that the much-loved nurse suffered multiple wounds, including blunt force trauma to the brain, and the final blows Davey inflicted were to stomp twice on the back of her neck.
Mrs Woodford had lived and worked in Fregon for five years, and community leaders told the court that Davey would never be welcome back on SA's indigenous lands.