Kearney starts at full-back in a back-three which also includes Shane Horgan and Fitzgerald, with Fergus McFadden partnering Gordon D'Arcy in the centre.
Eoin Reddan lines up alongside Shaun Berne at half-back.
In the pack, skipper Leo Cullen starts alongside Nathan Hines, with Heaslip forming a powerful back row alongside two recent Academy graduates, Sean O'Brien and Kevin McLaughlin.
Cian Healy continues in the front row alongside John Fogarty and Stan Wright.
The replacements bench will be confirmed closer to kick-off and the list features four Ireland internationals.
Speaking ahead of the Murrayfield encounter, young flanker Kevin McLaughlin said that healthy competition in the squad has kept everyone on their toes each week.
"My goal at the start of the season was to play the first three games so I'm delighted to have done that, but I know that the hard work starts now," he admitted.
" If you look at the back row you have players like Sean O'Brien, Stephen Keogh, Shane Jennings and now Jamie Heaslip all fighting for places and that level of competition is healthy because you know that you have to perform every time you step out on to the field.
"Rocky (Elsom's) departure certainly provided me with an opportunity and I'm enjoying every minute of it.
"He set a very high standard in his time here and that's what I have to aim for when I play.
"Every week is a learning curve for me and last weekend was a case in point. When you come up against the likes of Marty Holah, Jerry Collins and Filo Tiatia they teach you a thing or two, but it's great experience and I'm enjoying coming up against strong back row units every week."
McLaughlin added: "We have played against Edinburgh so often now that we know each other well.
"They play an expansive game and they're not afraid to use a fast offload game, so we will need to cut down on the space they have to manoeuvre in what I'm sure will be an open contest.
"There has been a good buzz around the camp this week with the Lions players returning and there were huge numbers in training in the early part of the week, which is good because it adds to the competition.
"We know that we will have to raise our game again against the league leaders, but it's a game we're excited about and are going to approach in a positive frame of mind."
LEINSTER (v Edinburgh): Rob Kearney; Shane Horgan, Fergus McFadden, Gordon D'Arcy, Luke Fitzgerald; Shaun Berne, Eoin Reddan; Cian Healy, John Fogarty, Stan Wright, Leo Cullen (capt), Nathan Hines, Kevin McLaughlin, Sean O'Brien, Jamie Heaslip.
Replacements (from): Bernard Jackman, Mike Ross, Devin Toner, Shane Jennings, Dominic Ryan, Simon Keogh, Jonathan Sexton, Girvan Dempsey.