Stoddart comes in for Garan Evans while Mark Jones, replacing Darren Daniel on the wing, is the only other change in the backs.
"Morgan deserves his chance with the Scarlets," said Director of Rugby Phil Davies. "He's been in great form for the semi-pro side. He's strong and elusive and offers us something different."
Stoddart is looking forward to the challenge which awaits him: "It's a big step up but it's a challenge I can't wait for. Hopefully I can rise to the occasion."
In the forwards there is an entirely new front row with Iestyn Thomas, Matthew Rees and Deacon Manu coming in while Gavin Thomas returns to the back row in place of James Bater.
Llanelli Scarlets: B Davies; D James, R King, G Evans, M Jones; S Jones, D Peel; I Thomas, M Rees, D Manu, V Cooper, I Afeaki, S Easterby (capt), G Thomas, A Popham
Replacements: A Gravelle, C Dunlea, A Jones, N Thomas, C Stuart-Smith, C Thomas, M Watkins
Ulster Rugby: B Cunningham; A Maxwell, P Steinmetz, P Wallace, A Trimble; D Humphreys, I Boss; J Fitzpatrick, R Best, B Young, J Harrison (capt), M McCullough, N Best, S Ferris, R Wilson
Replacements: P Shields, S Best, T Barker, K Dawson, K Campbell, K Maggs, S Young
Referee: Tony Spreadbury (England)