PA-28-180 Flight Instructor reported a near mid air collision with a helicopter on a converging course immediately after becoming airborne from a tower controlled field. Instructor took controls and made an evasive maneuver to avoid the helicopter.

Narrative

Me and my student who is a student pilot had a flight planned to work on some maneuvers in our practice area which is north-west of ZZZ. We started the airplane up received our taxi clearance and began to taxi down taxiway 1 to runway XX. We needed to still do our run up so we turned around into the wind on taxiway 1 parallel to taxiway 2. We then noticed a PC-12 taxing back to runway XX and ground instructed us to do our run up on taxiway 2; so we did. After we completed the run up we decided we can depart from taxiway 2 and requested takeoff clearance from there. Tower then told us to hold short for landing traffic so we did; then tower advised that he had two more airplanes on short final for both runway XX and runway XY and that after they landed that he would clear us to take off so we waited. Once those planes had landed we sat for almost another 10 minutes until we noticed another PC-12 taxing down taxiway 1 and was holding short of runway XX at taxiway 1. That aircraft then proceeded to request takeoff clearance and was given the takeoff clearance. I then thought maybe tower had forgotten about us so I reminded them we were still waiting and they responded with 'we will get you out shortly' so we waited some more. Finally after what seemed like sitting on taxiway 2 for 30 minutes we were given a takeoff clearance with a 'no delay' instruction. So we repeated it and pulled out on to runway XX and off we went. After reaching take off speed and rotation; I reminded my student about our climbing airspeed and not a couple seconds after that as I was scanning; I saw a military helicopter same altitude on a converging course with us about 300 to 350 feet away and closing. I then told my student 'my controls' and made a climbing right run to try to avoid the helicopter. I then noticed the helicopter flew right underneath us estimating about 250 feet below us. I then asked tower for a phone number; and calmed myself down to continue with my flight lesson. After the flight the controller met me in the FBO to apologize.