The woman - who hasn’t been named - will receive the cash from Lanarkshire Acute Hospitals NHS Trust following a Court of Session judgement.
The award was given by judge Lady Rae following a case that was heard at the Edinburgh based court earlier this year.
It is claimed by the woman that staff at Law Hospital’s maternity unit acted negligently when her son was born there in July 1999.
She claimed the actions of midwife Sister Rosemary Murphy caused her son to sustain a serious shoulder injury.
Lady Rae agreed and ordered the board to pay the mum of two compensation.
In a judgement issued at the court on Thursday, the judge wrote about the woman’s recollections of the moments leading up to the little boy’s birth.
She wrote: “She then became aware of Sister Murphy trying to deliver the baby. She saw her stand back apparently in thought.
“Sister Murphy then took a step forward and pulled the baby out. The pull was ‘pretty violent’. “Sister Murphy looked as if she was taking part in a ‘tug of war.’”
The case was heard in court earlier this year. The woman’s lawyers claimed that the injury suffered by the little boy was caused by Sister Murphy.
The court heard how the little boy was born on July 1999 at Law Hospital’s William Smellie Maternity Unit.
Initially, a student midwife attempted to deliver the boy, who is called C in the judgement.
But the trainee was unable to deliver the infant, prompting Sister Murphy to take over.
After the little boy was born, doctors diagnosed him with a ‘severe brachial plexus injury’ which resulted in him being left with a permanent disability.
Lawyers acting for the woman claimed in court that Sister Murphy didn’t follow correct procedures when she was delivering the boy.
Lady Rae described the evidence that was given in court about the birth and how a student midwife called Lynn Kerr was involved in the birth.
She wrote: “Prior to the commencement of the second stage she was asked if student midwife Kerr could undertake the delivery of the baby.
“Accompanying the student was Sister Murphy. There was also a student nurse present in the room.
“When the baby’s head emerged, the pursuer thought that the student midwife looked ‘panicked.’
“She asked what she should do as the cord was round the baby’s neck. Sister Murphy moved over and instructed the student to attempt to manoeuvre the cord over the baby’s head.
“There was a pause and someone said ‘right push with the next contraction.’
“The student midwife appeared timid and the pursuer heard her say words like ‘it’s not moving’ or ‘it’s not happening.’
“The pursuer was still being told to push. She then became aware of Sister Murphy trying to deliver the baby.”
Lawyers acting for the hospital denied liability.
However, Lady Rae ruled there was enough evidence to prove that Sister Murphy acted wrongly.
She wrote: “I am satisfied that in course of his birth, C suffered a severe brachial plexus injury to his right side as a result of the negligence of the defenders’ employee Sister Rosemary Murphy and for whom the defenders are responsible.
“Sister Murphy failed to recognise an obstetric emergency after the student midwife had been unable to deliver the body of C after delivery of his head; she failed to summon help in accordance with the protocol in existence as at July 1999.
“As a result of these failures C was born with a severe brachial plexus injury to his right shoulder.”