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."

Opener Stuart Thompson hit 56 while Gary Wilson (41 no) and captain William Porterfield (39) added valuable runs as Ireland made 165-5 in Greater Noida.
It was not enough with Samiullah Shenwari (56) and Mohammad Shahzad (47) helping the Afghans to 171-4 with two overs to spare.
The sides meet again in the second T20 at the same venue on Friday.
Ireland suffered an early blow when opener Paul Stirling was dismissed for a duck and with just one run on the board.
Thompson and Porterfield steadied the innings before Wilson helped the Irish to a competitive total.
Shahzad and Najeeb Tarakai (27) put on an opening stand of 51 as Afghanistan cruised to their victory target.
Afghan spinner Amir Hamza (2-23) was the only bowler to take more than one wicket on a day when the bat dominated.
"We fell a little bit short of potentially a very big score. We could have added another 15 and gotten up to the 180 we were looking for," said Porterfield.
"As well as we played I thought we just came up short with the ball. We didn't quite execute things as well as we would have liked."
The loss of paceman Boyd Rankin for the T20s, because of a back problem, was another setback for the Irish on Wednesday.
Rankin is expected to return for the five ODIs against Afghanistan, starting on 15 March.
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.
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Ireland started the three-match T20 series against Afghanistan with a six-wicket defeat in India on Wednesday.