Morgan shone in the Lambs' 1-0 FA Cup win over Cheltenham but has missed the last two games due to international duty with the Northern Ireland Under-21 squad.
"We are delighted," Tamworth boss Dale Belford told the club's official website.
"David is a quality midfielder, someone who really gets around the park and has a lot of energy.
"We were really impressed with him but had to lose him to Northern Ireland for a couple of weeks.
"It's great to have him back on board now ahead of the weekend trip to Kidderminster. He's here until January and we will then maybe look to extend it further."