Mrs Palasics and her husband Gregor were at their McKellar home on the evening of November 6, 1999, when two men forced their way in and bound and savagely beat them.
The men ransacked their home and stole cash and jewellery.
The 72-year-old did not survive her injuries and died at the scene.
Key to the investigation were two previous incidents where the Palasics were victims of a burglary in 1997 and an aggravated burglary in 1998 when they lived in Red Hill, another Canberra suburb.
A reward of $500,000 was offered in 2012, and police subsequently released information relating to footwear worn by one of the offenders.
A relaunched investigation led to the arrest of a 68-year-old man at his home in Rowville in Melbourne on Wednesday.
He is expected to be extradited to the ACT in coming days.
The family said in a statement it had been "24 years of pain".
"We have never given up hope of finding out who was responsible for this heinous act," they said.
"Thanks to the efforts of the criminal investigation unit of the AFP and commitment of AFP commissioner, Reece Kershaw, one of the alleged offenders involved in the murder of my grandmother is finally facing justice."
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