Like many events in history, the question of "how long" presents a challenge to answer. Dates in history are often more arbitrarily the result of a consensus of opinions of historians than actual concrete dates. For example, the signing of a treaty contains the date when a treaty is signed, and with certainty a historian can say a treaty to end a war was signed on this date. However, this does not mean fighting ceased at the exact moment the treaty was signed. It may be days, weeks, or months after the treaty is signed before fighting actually ends. Communicating the end of a war in time past was not as easily accomplished as it is today with modern technology. So, having recognized the problem with dating events occurring over time, how long did it take for Rome to conquer all of its land?
Historians generally agree the Roman Empire began somewhere around 31 BCE and began to break apart in 476 CE when the German Goths defeated the Romans, leaving only the Byzantine Empire intact. You could put forth the argument that it took Rome 507 years to conquer all their land if you take the position that during the time of the dominance of the empire, Rome was in a constant state of conquering, putting down insurrection, and expanding by consolidation. Arguably, once the Roman Empire was forced to accept a defensive posture, they no longer were able to sustain an offensive presence and conquer new territories or maintain the remaining territories comprising the empire.
Another way to look at is from the "Pax Romana" (Roman Peace), which historians date between 27 BCE to 14 CE—200 years. If this perspective is accepted, then one could argue that all of the Roman conquests were completed in less than 300 years, with the years of peace representing the completion of the conquests. The territories under Roman rule were relatively peaceful, and little or no expansion of the empire was occurring, as Rome occupied most of the known world during that time.
A third way to answer the question is to remove the word "conquer" and replace it with "consolidate." Rome was by nature an imperialistic juggernaut. As Rome expanded, smaller territories were subsumed into the Roman Empire with no resistance. The smaller territories either had no capacity to resist or found an advantage by being part of the empire. For example, they may have wanted Roman rule for protection from more hostile forces than the Romans or for various economic advantages Roman governance provided to stabilizing the economic system. Historians believe imperial Rome lasted for 1,500 years, whereas the Republic version of Rome lasted for 500.
Depending on which view of Roman conquest you hold, the answer is between 200 and 1,500 years.