A good DMM will read the RMS value, which is the root of the mean of the squares, this is derived from the equation for power (V^{2}/R for voltage over a resistor), Wikipedia (link above) has the proper derivation. But for a square wave, the RMS and average value are actually identical, so for this purpose, you might as well use the average voltage. For a square wave from 0 to Vpp with a 50% duty cycle, the average voltage is Vpp/2. So ~1.5V RMS/average corresponds with 3Vpp. I assume that you use a 10x scope probe, which attenuates the signal ten times (voltage divider, 9Mohm / 1Mohm). So the 3Vpp becomes 300mVpp.

An average responding meter will multiply the average with 1.1 to correct for the difference between RMS and average for sinusoidal signals, but many average responding meters won't have the bandwidth for 1kHz square wave anyway (something like 10kHz might be OK, many cheap ones are just 50-500Hz), so I wouldn't trust their answers, although the results from your Fluke 17B (which is not true RMS if I remember correctly) seem plausible in this case, maybe the frequency roll-off and +10% correction cancel each other out.