The 21-year-old left-back joins the Edinburgh club on a season-long agreement after his parent club extended his contract until summer 2022.
Having secured loanees Ross Stewart and Josh Ginnelly on permanent deals, Cochrane is the latest recruit to join Robbie Neilson’s squad for a return to the Cinch Scottish Premiership.
He spent last season on loan at the Belgian club Union Saint-Gilloise, although his time abroad ended prematurely due to an ankle injury. He underwent rehabilitation and is now ready to continue his career in the Capital.
Despite Hearts’ city rivals Hibs recently announcing a formal player development partnership with Brighton, the English Premier League club are sending Cochrane to Tynecastle for the next 12 months.
“I’m delighted to get the deal done for Alex to join us for the season ahead,” Neilson told the Hearts website. “He’s a very highly-rated player with a good pedigree so I’m looking forward to working with him.
“He’ll provide competition in the left side of defence, and his arrival also gives us the flexibility to change formation should we need to.”
Hearts sporting director Joe Savage said: “We saw off competition from other clubs to get Alex’s signature so this deal is a bit of a coup for us.
“He’s experienced first-team football with Brighton and also spent a season playing abroad so we know he’s a talented player with bags of potential, and we believe he is the right fit for Hearts.
“Developing links with established Premier League sides like Brighton could be really important for us in the future, so I have to thank them for their assistance with this move.
“It’s been a long process to get this done but we are really excited to have Alex in the building.”
Former Hearts defender David Weir is Albion’s loans manager and believes a year in Scotland could benefit the full-back, who has represented England at under-20 level.
Cochrane was born in Brighton and came through Albion’s youth academy before a first-team debut in the Carabao Cup against Aston Villa in 2019.
Speaking last month after extending the player’s contract, Weir said: “Alex had a really good experience out in Belgium with Union and, as he’s spoken about, it has been really beneficial for both him as a person and as a footballer.
“While that development was curtailed slightly by injury, he showed how well he can adjust and learn during his time out on loan, which is a testament to him, especially during the pandemic. I am pleased to see he will be continuing his development with us.”
Hearts are still awaiting the return of left-back Stephen Kingsley from the groin injury which ended his season early.
He is expected to resume full training soon and could take part in the club’s first competitive match of the new campaign, which comes on July 10 in the Premier Sports Cup at Peterhead.