Morgan, who last week scored a try for his country against Tonga, comes into the midfield as Head Coach Bernard Jackman makes five changes to the team that faced Connacht last time out.
Wing Jared Rosser is named on the wing after recovering from injury while Hallam Amos, who also returns from his time in the Wales camp, moves to the other flank.
Three changes in the pack include a welcome return for back row dynamo Ollie Griffiths who starts at Number Eight for the league encounter.
Lock Rynard Landman is handed a recall in the second row while the final change sees Ryan Bevington at loosehead prop, where he packs down alongside skipper Richard Hibbard.
Wales international Leon Brown returns on the bench while fit-again duo Arwel Robson and Brandon Nansen join scrum half Rhodri Davies and back row James Benjamin among the replacements.
“This is a massive game for us and it’s great to welcome back the likes of Ollie, Jared, Brandon and Arwel and also a number of our Wales internationals,” said Jackman.
“We know the challenge ahead of us. The two Scottish teams now have real depth to their squads, as Scarlets and Ospreys both found out in the last round.
“Edinburgh are a very physical team who don’t take many risks, they are very similar to Leicester of six or seven years ago. They kick well, play territory and are solid defensively.
“Their European game against Toulon was the best they have played all season and they ripped them apart.
“Every game in the Guinness PRO14 is tough now and we will need to be at our best to get the right result. But we are excited about getting back home in front of our support.”
Dougie Fife, Darcy Graham, James Johnstone, Chris Dean, Duhan van der Merwe, Simon Hickey, Henry Pyrgos; Pierre Schoeman, Ross Ford, Pietro Ceccarelli, James Hodgson, Callum Hunter-Hill, Ben ToolisAlly Miller, Luke Hamilton.
Replacements: David Cherry, Rory Sutherland, Murray McCallum, Callum Atkinson, Lewis Wynne, Sean Kennedy, Jaco van der Walt, Juan Pablo Socino