The injury-jinxed Wales full-back returns after rupturing his Achilles tendon for the Dragons' Magners League clash at Rodney Parade.
But Morgan came through unscathed after a 30-minute outing in the Dragons' development match with Welsh rivals the Ospreys on Monday and will start on the bench.
Dragons coach Paul Turner said: "Kevin's been really unlucky with injuries but he came through okay on Monday.
"He showed us the old Kev with the step and the dart. He has taken a lot of contact and come through training without a problem.
"We had hoped he would be ready for Toulouse in December and time has gone along. But it has allowed young Jason Tovey to develop.
"Lots of players do not recovered from Achilles injuries and it can't have been easy for him but he's been patient. He's a real talent for us."
Morgan, capped 48 times by Wales, has undergone reconstruction of both knees as well as suffering a broken jaw, foot surgery and an ankle operation in the last three years.
But while there is good news for Morgan, the Dragons will be without Luke Charteris who remains on Six Nations duty with Wales although bad boy prop Rhys Thomas starts.
Turner said: "We would love to have Luke in our side but we must deal with that. He showed his quality when he came on against Scotland. He's got a big future ahead of him.
"We're delighted to see our players in the national side but we want more of them. It will take time."
The Dragons lie just one point above the Irish province as the Gwent region aim to secure automatic Heineken Cup qualification.
But Turner is wary of the challenge Matt Williams' resurgent Ulster will pose.
Turner said: "The goal is to be the top Welsh side and the next two games against Ulster and Munster are must-win games for us.
"If we can pick up eight-ten points then it will push us up the table and other sides will be looking around them.
"But Ulster are strong up front and did everything right in the win over Munster at Thomond Park - it could have been 100 points.
"That's as good as it gets but they have taken it further by beating Harlequins and pushing Stade Francais all the way in Europe. It's a huge game for us on Sunday."
Dragons: J Tovey; M Thomas, R Gomer Davies, A Smith, R Fussell, S Connor, W Evans; A Black, T Willis (capt), R Thomas, A Jones, H Macdonald, J Bearman, L Evans, R Parks
Replacements: S Jones, N Hall, A Hall, G Webb, P Dollman, K Morgan, R Lewis.