Named locally as Mirko Marweg, 58, and Luis Aldarondo Jr, 37, were changing a wheel on the aircraft when a tyre exploded, and a third person was injured during the incident.
The International Association of Machinists and Aerospace Workers issued the following statements: "We will offer our resources to all those impacted by this tragic event. We call on Delta and the relevant authorities to quickly launch a thorough investigation into how this happened".
The airport said its "prayers are with the families affected by the tragic incident".
Mirko Marweg had served in the army for four years and was previously employed by the Atlanta Rapid Transit Authority. Luis Aldarondo leaves behind a young family.
The airline said: "The Delta family is heartbroken at the loss of two team members and the injury of another following an incident this morning at the Atlanta Technical Operations Maintenance facility.
We have extended our full support to family members and colleagues during this incredibly difficult time."