The English Premier League club’s recently-appointed technical director David Weir, the former Hearts and Scotland defender, confirmed the decision earlier today.
Cochrane, 22, is now contracted to Brighton for a further 12 months and must wait to learn whether he is part of manager Graham Potter’s first-team plans for next season.
By extending his deal, Brighton have protected their investment in the player, who has a number of interested suitors both in Scotland and England.
He made 40 appearances for Hearts during the season just ended, scoring three goals, and impressed as a versatile and attack-minded left full-back.
He played as a wing-back and even in central defence as the Edinburgh club enjoyed one of their most memorable campaigns in living memory.
Cochrane experienced derby matches against Hibs, plus a Scottish Cup final and semi-final as Hearts qualified for next season’s Europa League play-off round.
Brighton have also given extended deals to Cochrane’s fellow under-23 players Tom McGill, Jack Spong, Lorent Tolaj and Ben Wilson.
Midfielder Pascal Gross signed a new two-year contract earlier this afternoon, and striker Danny Welbeck is expected to sign a new contract this summer.
“We are delighted that Pascal and Danny will be with us next season,” Weir told the club’s website.
“Both are important members of Graham’s squad, having each had another excellent season in the Premier League, playing key roles in helping us secure our highest-ever top-flight finish.”