The game will also mark O'Driscoll's 100th appearance for the province and with the right result, they could be on the cusp of securing their first league title under coach Michael Cheika.
O'Driscoll will partner Felipe Contepomi in Leinster's midfield and in the only other change to the back-line that started the 21-12 victory over Munster last Saturday, Luke Fitzgerald moves to the right wing as Shane Horgan is ill.
Trevor Hogan will line up in the second row in a pack that also shows two changes, with Stephen Keogh forming the back row alongside Shane Jennings and Jamie Heaslip.
The Leinster replacements bench will be confirmed an hour before kick-off.
Looking forward to his return and the title run-in, O'Driscoll said: "As we approach these last few games it's important that we don't think about where we are and treat every game on its own merit. The position in the table shouldn't affect our mindset or how we approach games.
'Friday's game will be a great occasion. Our support this year has been fantastic and great credit must go to the Leinster public for supporting the side, particularly when the team has been missing some international players.
"The support that we have received over the years has gone from strength to strength and it does give the team a huge lift.
"I hope that our supporters continue to back the team and we will be doing our best to try and bring some silverware home for them all," he added.
LEINSTER (v Edinburgh): Girvan Dempsey; Luke Fitzgerald, Brian O'Driscoll, Felipe Contepomi, Rob Kearney; Jonathan Sexton, Chris Whitaker; Ollie Le Roux, Bernard Jackman, Stan Wright, Leo Cullen (capt), Trevor Hogan, Stephen Keogh, Shane Jennings, Jamie Heaslip.
Replacements (from): Brian Blaney, Stephen Knoop, Malcolm O'Kelly, Cameron Jowitt, Keith Gleeson, Chris Keane, Christian Warner, Michael Berne, Gary Brown.