MRS Koken, 56, had suffered from kidney disease and endured dialysis for the two years. She had been told by doctors that she would not be able to survive much longer without a kidney transplant.
Mr Basaran's wife Funda said that all family members and close relatives were tested for a match and that only her husband's was deemed suitable.
``Baris had no qualms,'' Mrs Basaran said. ``He agreed to donate his kidney without any persuasion.''
The transplant was carried out at Westmead Hospital in two stages last week.
The first stage involved the removal of Mr Basaran's kidney while the second involved placing it in Mrs Koken.
Both operations were deemed a success and the pair are now recovering at home.
Mrs Basaran said she was pleased by her husband's kindness, saying he has first made her happy when their daughter, Leyla was born three months ago.
``He has given my parents their first grandchild and now gave my mum, Nese, a new lease on life,'' she said.
``My parents, all relatives and I are very impressed with Baris especially Mum.
``He's now her favourite son-in-law. She's alive and in good health today because of him.''
Both patients must return to the hospital for blood tests, initially once every two weeks, and later once a year, to ensure the kidney is working properly.
The families thanked doctors, nurses and supporting staff involved in the operations.
Mrs Koken's husband, Saim, 66, said Baris's kindness made his family very happy.