The 18-year-old joins the Dens Park outfit until the end of the season.
Dundee are 14 points adrift at the bottom of the SPL and boss Barry Smith is hoping to add a striker.
A statement on the club's website confirmed: "Dundee football club are very pleased to announce the signing of David Morgan on loan from Nottingham Forest until the end of the season.
"The-18-year old midfielder has already represented Northern Ireland at Under-21 level.
"The club can confirm they are still in pursuit of at least one striker that will not necessarily be affected by the transfer window."
Meanwhile, Dundee defender Neil McGregor has joined Ayr United on loan until the end of the season.