Captain reported observers informed the flight crew of a significant amount of fuel was seen venting from the aircraft on take off. The flight crew performed an air turn back and precautionary landing at departure airport after it was determined that all of the fuel in the center tank had vented overboard.

Narrative

Note: I'm submitting this at the request of the Dispatch Chief Pilot; with whom I debriefed after the flight. He asked me to submit a report for data collection purposes. Shortly after an on-time takeoff from ZZZ Runway XXR (about 6;000 feet MSL; while climbing out and bound for ZZZ1; we were advised by Departure Control that a (Company) aircrew from a flight behind us wanted to alert us that we had been venting a very large amount of fuel from our right wing fuel vent; from about the beginning of takeoff roll; and that it had continued for as long as the crew could observe us. My First Officer (Pilot Monitoring) visually confirmed this; stressing that we were indeed venting a lot of fuel. We had heard part of the aircrew's transmission before being advised we were the subject of discussion; and we recalled that the reporting crew sounded calm and professional; but clearly considered it urgent that we understood we were venting fuel at an uncommonly high rate. When flight deck duties permitted; FO (First Officer) used his cell phone to video the venting fuel so I could see it; too. I agreed that it was abnormal; and we coordinated with ATC to level off at 10;000 feet MSL to assess our situation and make a game plan. The high rate of fuel venting appeared unaffected by my power reduction during the level-off at 10;000 feet and would ultimately continue to vent at the same high rate until our center fuel tank was completely empty (over an hour later). There is no checklist for this anomaly; as there was no fuel imbalance (full wing tanks and about 10;000 pounds center tank fuel); and the circumstances did not meet the conditions to qualify as a fuel leak. My FO and I agreed not to proceed to ZZZ1 with an undiagnosed fuel issue while appearing to be jettisoning more fuel that we could afford to lose over the course of an approximately three hour flight. We advised ATC that we still had fuel venting and that we did not need to declare anything; but that we would require holding while formulating a game plan for return to ZZZ. We advised our F/As (First Officer); Dispatch and passengers of the situation and calmly explained to everyone that the venting fuel was the result of a normal aircraft fuel venting function that was simply working overtime for reasons unknown to us.While being vectored and awaiting holding; I noted the current total fuel quantity; kept the power (i.e.; engine fuel flow) near constant; hacked the clock and determined how much time it took to burn 1;000 pounds of fuel so we could then subtract what the engines burned in that time frame from the total decrease in fuel quantity; then calculate the approximate rate of venting fuel; which we determined to be about 750 pounds per hour. We accepted holding at the ZZZZZ fix at 8;000 feet; which I considered high enough (above 5;000 feet AGL for fuel dissipation above the ground) and low enough for burning gas quickly; which we did with landing gear down and Flaps 5 after entering holding. We decided to burn fuel down to the new (146;300 pounds) -800 maximum landing weight before considering returning to ZZZ for landing. I was aware that an overweight landing is acceptable if landing data supports it; but I was not willing to consider doing so with the fuel still venting; as we felt we had to assume the fuel would still be venting during landing and taxi (I did not favor the risk of venting warm fuel on very hot concrete after stopping with brakes warmer than necessary from landing overweight). As it happened; the venting stopped immediately when center tank fuel was depleted; which coincided with our total weight being right at the new max landing weight. We then departed holding and landed uneventfully on Runway XX. We never declared anything; but we advised Approach we'd like the Fire Department to look us over after clearing the runway. They did so and observed no problems with our aircraft. I cleared them off; but they then asked if one of them couldfollow us to the gate; which we allowed. Block time was just under two hours. I debriefed by phone with Dispatch/Chief Pilot/Maintenance; put the write up in the logbook; debriefed with local Maintenance and proceeded with my crew to our new gate to fly uneventfully to ZZZ1.