Niamh Maye was just 18 when she was last seen near Jingellic in southern NSW on March 30, 2002.
She was the youngest of seven children who grew up in Armidale, northern NSW.
She was planning to catch a bus from Batlow, then a train from Cootamundra to meet her sister in Sydney and travel home for Easter, but never arrived.
"It is suspected she met with foul play," NSW Police said in a statement on Wednesday.
Niamh was fruit-picking on a gap year when she left a campground in Jingellic, in a black Holden hearse with a fellow fruit-picker Jason "Jack" Nicklason.
Nicklason told police he'd last seen Niamh after leaving her by the road on March 30.
She was carrying a backpack with her clothing, camera, camping gear and cookware.
None of the items have ever been found.
Anne Maye said her daughter' disappearance had left a gaping hole in the family.
"Today Niamh should be celebrating her 40th birthday with her family and friends, instead we mourn the beautiful soul and precious time that have been taken from us," she said in a statement.
Her family needed to lay their daughter, sister, aunt and friend to rest "with the dignity and respect she deserves", Mrs Maye said.
"Words can't describe how special Niamh is to our whole family. Her disappearance has left a gaping hole and we have never given up on finding her."
The reward is being offered for information that leads to an arrest and conviction or the discovery of her remains.
Riverina Police District Commander Superintendent Andrew Spliet says he hopes the reward will be an incentive for anyone who knows something about Niamh's fate to speak up.
"Any information, no matter how small, could be the missing piece of the puzzle we need to locate Niamh and finally bring answers and some peace to her family," he said.
Nicklason - the man she was last seen with - was later arrested in Brisbane for the unrelated bashing and rape of a woman in October the same year.
While being escorted to a Brisbane jail cell, he escaped custody and fell to his death.
Police named Nicklason as a suspect in her disappearance.
A 2012 coronial inquest determined Niamh died at or near Tumut on March 30 or 31.
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