After the detection of gravitational waves from compact binary coalescences, the search for transient gravitational-wave signals with less well-defined waveforms for which matched filtering is not well suited is one of the frontiers for gravitational-wave astronomy. Broadly classified into "short"1 s and "long"1 s duration signals, these signals are expected from a variety of astrophysical processes, including non-axisymmetric deformations in magnetars or eccentric binary black hole coalescences. In this work, we present a search for long-duration gravitational-wave transients from Advanced LIGO and Advanced Virgo's third observing run from April 2019 to March 2020. For this search, we use minimal assumptions for the sky location, event time, waveform morphology, and duration of the source. The search covers the range of 2-500 s in duration and a frequency band of 24-2048 Hz. We find no significant triggers within this parameter space; we report sensitivity limits on the signal strength of gravitational waves characterized by the root-sum-square amplitude hrss as a function of waveform morphology. These hrss limits improve upon the results from the second observing run by an average factor of 1.8.