Renwick, a former Scotland Under-20 internationalist, joins from Southern Knights and has been registered for this weekend’s European Challenge Cup tie against London Irish, with Stuart McInally dropping out.
McInally suffered a neck injury during Saturday’s win over Cardiff and was taken off at half-time.
Edinburgh said McInally’s withdrawal from the squad to face London Irish was a “precautionary measure”.
The Scotland hooker missed last season’s Six Nations because of a neck injury but the latest issue is not causing undue concern and he is expected to return to full training next week.
Renwick, 24, was part of the Southern Knights side which reached the final of the FOSROC Super6 in October. He came through the youth system at Hawick and played senior rugby for the Greens and more recently Watsonians.
Dave Cherry replaced McInally against Cardiff and is expected to start against London Irish in Brentford on Saturday. Edinburgh also have Adam McBurney and Patrick Harrison in reserve.
Currie, meanwhile, has spoken of his delight at putting pen to paper on his first pro deal.
“It’s an opportunity that I’m really excited about,” he said. “I’ve been in the Academy for the past few years and I've been around Edinburgh for a while now so to sign for the club is pretty massive.”
The 20-year-old from Dumfries-shire made his breakthrough last season, coming on as a late substitute for his Edinburgh debut in the Pro14 loss to Munster at Murrayfield. He then scored his first try for the club in the Rainbow Cup win over Zebre in April.
He played at outside centre in the away win over Dragons in the United Rugby Championship this season and retained his place for the home victory over Benetton the following week, keeping Mark Bennett out of the starting XV.
Currie admitted that it had been a surreal experience given the way Bennett has helped oversee his development at the club.
“Mark Bennett has always been one I have looked up to,” said Currie, who came through the ranks at Dumfries Saints RFC and then Merchiston Castle School.
“It was a bit surreal when I first came in. I was playing alongside him but he has been great as my role model and my mentor at the club. He has really helped me.”
Bennett has been excellent for Edinburgh this season and Currie knows he may have to bide his time.
Mike Blair has high hopes for Currie and the Edinburgh coach singled him out on Radio Scotland at the weekend as one to watch.
“I've not actually heard that but it is quite nice to hear,” said the player. “He has been great. He is really big on micro-skills - your catch-pass, kicking, etc. Those little things make such a difference to your game.
“We are constantly doing skills sessions, little bits here and there after training where you can really get a chance to improve. That's a great opportunity for me and a lot of the younger boys to develop that side of our game so you know when you need it in a match it is much smoother.”