Peter Temin has a historiographical essay on the estimation of Roman GDP, which is available online here.

The overly clear answer is that Roman Italy, based on our fragmentary evidence and a whole lot of inference from the urbanisation rate, was maybe about as rich as England or the Netherlands in 1600, about 1400$ (1990 $GK) per capita. Most of the rest of the Roman empire was pretty poor, a low multiple of subsistence (which is about $300)." That would make Roman Italy the richest society not only of its time, but until around the 10th-14th century, when the wealthiest states (Northern Italy, Song Dynasty China, Iraq during the Islamic Golden age, etc) would match, though not surpass, that level. No society would be decisively richer per person until the beginnings of industrialisation. But Roman Italy is not the whole empire.

The more nuanced answer is that there is nowhere near enough evidence to solidly reconstruct even the basic components of GDP for Roman times. Finding comparable measurements across the various parts of the Roman empire and across time for basics like "how much did a worker earn in a day" or "how much wheat was grown" is hard enough. Finding measures that are also meaningfully comparable to later societies is even harder, and there are serious critiques (such as Deng and O'Brien) as to whether this whole ancient GDP estimating exercise isn't just a fool's errand, even for much later periods. So we are stuck with an estimate that is more inference than solidly-evidenced calculation.

But the size of Rome itself suggests that the estimates on the high side can't be too far off. Basic Malthusian logic tells us that a city will not sustain itself if it cannot be fed, and the only way to feed it is with an agricultural hinterland not only productive enough to make the food, but which is also receiving something of equivalent value in return for that food. Rome must have traded for that food over a large area, which almost certainly means a highly integrated market society. There are not many cities of (approximately) a million people anywhere at all in the world at any point before 1800, and those places that do have such cities are among the richest societies.