Best will captain the province as they go in search of their first win in seven Magners League games.
Stephen Ferris is also set to start at blindside flanker, having overcome the rib injury which kept him out of last weekend's 25-18 defeat at Glasgow.
But Paddy Wallace is a notable absentee from Brian McLaughlin's selection, as a thigh injury keeps him on the sidelines.
The changes in the back-line see Jamie Smith return at full-back, Simon Danielli reverts to the left wing and Niall O'Connor gets the nod over Ian Humphreys for the out-half slot.
Best and Springbok prop BJ Botha will add strength and experience to the front row, with Andi Kyriacou and Declan Fitzpatrick making way.
Ryan Caldwell drops to the replacements bench, with Dan Tuohy drafted into the second row, and Ferris and Willie Faloon have been introduced into the back row, at the expense of Chris Henry and David Pollock.
Looking forward to the Murrayfield encounter, McLaughlin said: "We are all very positive heading over to face Edinburgh. We have played them quite a few times this season, the last time at Ravenhill we gained the points.
"In September, when we faced them in the league, we were narrowly beaten by three points. We had a really strong first half, but just couldn't sustain it, and that's been our problem over the last number of games - doing well early on, but just unable to sustain it until the final whistle.
"The players are training hard, and working well together. Everyone knows what is expected of them. Yesterday, the Ireland defence coach Les Kiss was up doing a lot of work with us, and our attack is solid.
"So, it is just a matter of going out at Murrayfield on Sunday with the attitude that we can gain the victory.
"We have to be mentally and physically tough and make sure we don't give away soft, cheap and easy points," he added.
ULSTER (v Edinburgh): Jamie Smith; Andrew Trimble, Darren Cave, Ian Whitten, Simon Danielli; Niall O'Connor, Paul Marshall; Tom Court, Rory Best (capt), BJ Botha, Ed O'Donoghue, Dan Tuohy, Stephen Ferris, Willie Faloon, Robbie Diack.
Replacements: Andi Kyriacou, Bryan Young, Ryan Caldwell, Thomas Anderson, Isaac Boss, Ian Humphreys, Nevin Spence.