B737-700
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Commercial; Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 489
Situational Awareness; Communication Breakdown; Confusion
ATC Issue All Types; Conflict Ground Conflict; Critical; Ground Incursion Runway
Flight Crew Requested ATC Assistance / Clarification
Human Factors; Procedure
We had just finished deicing and were taxiing for departure. There was one controller working all frequencies. As we were taxiing down Echo Taxiway toward [Runway] 5L for departure; we were cleared to depart and to turn left to heading 035. The First Officer acknowledged the clearance. We did the checklist and continued toward the runway. We were about halfway down Echo when we were cleared for departure.The controller seemed very busy with all the other activity on Ground and Tower. Controller was even trying to find a deice frequency for an aircraft that needed to deice. As we approached [Runway] 5L for departure; I looked to my left to clear final. That's when I noticed [another] aircraft that seemed to be very close to landing. The First Officer said that it was at 400 feet. I stopped the aircraft as we crossed the hold short line. The First Officer called Tower and informed them of the traffic on final and that we had stopped. Controller then sent the aircraft around. As the aircraft went around and all was clear; we were cleared for takeoff again. We departed and continued.
Pilot reported being cleared for takeoff while on a taxiway; turned onto runway and while turning; observed an aircraft on final.  Pilot advised Local Controller; who sent aircraft on final around.