The pair were among the first signings made by head coach Michael Bradley in the summer, with Leck joining Sean Cox in the move north from Sale Sharks and Black signing from Leeds Carnegie, all on one year deals.
Despite battling for selection with Scotland half-backs Greig Laidlaw and Mike Blair, Leck has grasped the chance to showcase his busy style and pin-point delivery to great effect during the international window, while the relentless attitude and abrasive physicality of up-and-coming Alex Black has seen him live up to his billing as a prospect with a bright future ahead.
Edinburgh Rugby head coach Michael Bradley said: "Both players have worked very hard this year, have been extremely professional and patient for their chances to play and have performed well when those opportunities have come their way.
"Their work ethic and level of professionalism has been exceptional and they deserve this chance to further their careers at the club.
"We're delighted that they're staying on."
Leck has made 11 appearances for the club this season, earning praise as a player with urgency and accuracy at the forefront of his attacking armoury.
Before heading north, Leck (the son of Hawick head coach Phil) started out at Burnley rugby club and Preston Grasshoppers, as part of the early development stages of the Sale Sharks Academy.
During this time he played for the Lancashire district side (which he represented into senior rugby), England U16 and U18, before signing full-time with Sale aged 18, where he remained for six years until he moved to Murrayfield last summer.
He said: "Coming to Edinburgh was a very exciting prospect for me with a fresh challenge to work hard, get as many games as I could and prove my worth.
"It's a fantastic club and we play a fast-paced style of rugby that really suits my game.
"The club have made some top quality signings in recent weeks so it's a nice feeling to know I'm going to be part of an exciting future at the club."
In his first season of professional rugby north of the border, Inverness-born Alex Black has made three appearances for the club, including a debut in the 1872 Cup derby against Glasgow Warriors on New Year's Day.
Time is on the side of the 22-year-old who has impressed at every age-grade for Scotland from U17 to U20 while at former clubs Leeds Carnegie and getting exposure to the Aviva Premiership and Amlin Challenge Cup before signing for Edinburgh Rugby.
He now targets muscling his way into contention at Murrayfield and emulating the progress of former age-grade teammates David Denton and Matt Scott (who made their RBS 6 Nations debut this season) and the recently A-capped Tom Brown and Stuart McInally.
He said: "So many young players have improved massively under Michael [Bradley] who has shown that if you're good enough, you're definitely old enough.
"A lot of their success is down to that trust and confidence shown in their abilities and the knowledge that we'll give everything to play.
"I'm thrilled to have extended my time at the club. It means that I can really settle down, focus on my rugby and look to repay the faith shown in me so far."
Edinburgh Rugby new signings: WP Nel (Free State Cheetahs), Greig Tonks (Northampton Saints), Ulises Gamboa (Aironi, to the end of the season)
Edinburgh Rugby re-signings: Alex Black, Tom Brown, Sean Cox, Geoff Cross, David Denton, Grant Gilchrist, Robin Hislop, Gregor Hunter, Lee Jones, Greig Laidlaw, Chris Leck, Harry Leonard, Stuart McInally, Lewis Niven, Matt Scott, Steven Turnbull, Tim Visser