His return to full fitness allows Craig Ronaldson to shift to out-half where he forms the half-back pairing with Kieran Marmion.
The Galway-born Tiernan O'Halloran has been named to start on the left wing and features in an all-Irish qualified back-line.
Up front, Connacht's most-capped player Michael Swift is brought into the second row. His introduction means that Andrew Browne moves back to openside flanker.
Number 8 John Muldoon will captain the side at the Sportsground on Saturday evening.
Speaking about the team selection and this weekend's game, head coach Pat Lam said: "It's a great boost to have Dave (McSharry) back from injury. He came through the Eagles game last week and his experience will be valuable against Edinburgh this weekend.
"Tiernan (O'Halloran) is a player who has worked hard to earn his place in the team. He went away to work on certain aspects of his game over the last few weeks and it was clear from his performance with the Eagles that he deserves this start.
"With such a physical game expected against a team like Edinburgh, it's good to be able to call on 'Swifty' for his experience and grunt up front.
"It was a short week and we had to put the disappointment of Glasgow quickly behind us. It was another opportunity missed, we know that. But it's fantastic to be back on our home pitch this weekend.
"We haven't had a game in front of our home fans in five weeks. The team are very much aware of what we have to do for Connacht Rugby and its supporters tomorrow."
The round 14 fixture is not on TV so the only way to get in on the action is to get down to the Galway stadium. Tickets start at just €20 for adults and it is €5 for all juniors. Click here to purchase tickets online.
Tickets can also be purchased from the Connacht Rugby office and from Centra and SuperValu stores province-wide.
CONNACHT (v Edinburgh): Robbie Henshaw; Fionn Carr, Eoin Griffin, Dave McSharry, Tiernan O'Halloran; Craig Ronaldson, Kieran Marmion; Denis Buckley, Jason Harris-Wright, Rodney Ah You, Michael Kearney, Michael Swift, Andrew Browne, Jake Heenan, John Muldoon (capt).
Replacements: Dave Heffernan, Ronan Loughney, JP Cooney, Aly Muldowney, George Naoupu, Paul O'Donohoe, Dan Parks, Darragh Leader.