The 33-year-old, a one-time England hopeful when Eddie Jones was in charge, joined the Irish province last summer following the massive clear-out that took place at the Chiefs.
The 22-year-old Irish-qualified Morgan has struggled to get a game for the Hurricanes this season, with All Black Brett Cameron establishing himself as the first-choice No10 and Ruben Love able to cover full-back and fly-half.
Edinburgh exited the EPCR Challenge Cup after suffering a 36-30 quarter-final defeat against the Sharks in Durban.
Leinster continued their 100 per cent start in the Investec Champions Cup with a crushing victory over Stade Francais on Saturday.
Ulster staged a second-half fightback to beat Zebre Parma 40-36 and get their United Rugby Championship campaign off to a winning start at Stadio Sergio Lanfranchi.
URC finalists Munster have revealed their full list of end-of-season leavers, with five more names added to the group that already included Malakai Fekitoa and Ben Healy.
Ejected from the Stade Francais academy at 19, Antoine Frisch has taken a circuitous route to success at Munster
Irish provincial heavyweights Leinster and Munster have named their teams for the Irish URC derby that will be played out in front of over 43,000 people at the Aviva Stadium this weekend.
Every team in the URC has been busy sorting transfers ahead of the upcoming summer break. The Irish provinces have been using their academies...
EPCR statistics show that the home side's in this weekend's Heineken Champions Cup quarter-finals will enjoy a significant advantage over their visitors.