Radwan Hamed collapsed during a game in Belgium in 2006. Last year a judge ruled Spurs breached its duties to him.
In a screening prior to signing for the club, an electrocardiogram test showed his heart was "unequivocally abnormal" but he was not stopped from playing.
The club regretted a former employee had been remiss in their duties.
In a statement, the family of Mr Hamed, who is now 27, said they were "relieved" a settlement had been reached, following a decade-long legal battle .
"Just as Radwan had no choice but to start his difficult journey towards recovery, we had no choice but to start the difficult journey to obtain justice," they said.
"We risked losing our home and faced personal financial ruin in order to pursue justice for our son.
"The club did not tell us or Radwan about his potentially fatal condition. Had they done so, Radwan would not have continued to play football."
The teenager collapsed during the game against Cercle Bruges on 4 August 2006 and was rushed to an intensive care unit but suffered oxygen starvation to his brain.
In the 2015 hearing, Mr Justice Hickinbottom ruled the club was 70% liable or Mr Hamed's injuries and Dr Peter Mills, the Football Association's regional cardiologist for South East England, was 30% liable.
The Premier League club will not be hit with a fee directly as their 70% portion was incurred by physicians they previously employed, who have agreed to indemnify the club.
Football Association rules require all football academy recruits to be referred to a cardiologist to help identify those prone to potentially fatal heart conditions.
Mr Hamed's MRI scan showed no obvious signs of hypertrophic cardiomyopathy, but Dr Mills wrote to Spurs saying the condition could not be excluded on these findings alone.
Eleven months later, the teenager, who was unaware his tests had revealed an "abnormal" heart condition, signed a contract with Spurs.
A spokesman for Spurs said: "The club wholeheartedly regrets that a former employee, as adjudged, was remiss in their duties to Radwan.
"This judgment will hopefully now secure the best possible treatment and care for him."
A Tottenham Hotspur youth player has agreed to damages, believed to be £7m, after he was left brain damaged from a cardiac arrest on his debut.