I'm not sure you can really state that thesis with certainty.
The world's top two religions are indeed monotheistic.
However, that could just be explained due to them both arising in the same region.
The third and fourth largest religions, Hinduism (1 billion adherents) and Shenisim (about 400 million), are both polytheistic.
The fifth, Buddhism (also about 400 million) either has no gods or is polytheistic as well, depending on how you want to look at it.
None of these really seem to be in any current danger of being replaced by a monotheistic faith.
One can also make a case that the two large Monotheistic religions were primarily spread by the sword, so its debatable how much their modern success has to do with their own internal qualities.
Nearly all countries where Islam is prevalent are either Afro-Asiatic-speaking countries, or were conqured/colonized by Afro-Asiatic speakers during the period they ran the trade routes to the far east and sub-Saharan Africa (and all such countries lie along those trade routes).
Nearly all countries where Christianity is prevalent are either Indo-European speaking, or were conquered and/or colonized by Indo-Europeans during their imperialistic age.
So if I were to have to put a time on this...
For Islam it would be the 8th to 11th centuries along the spice routes, and the end of that time for sub-Saharan Africa.
For Christianity there would be two major periods of expansion: one from the time of Constantine (4th Century) to the end of the Roman Empire (5h Century), some slow progress in Europe after that, and then another that started with the Age of Discovery in the late 15th century, and ended (most likely) with decolonization in the late 20th Century.
history.stackexchange.com/users/771/T.E.D.
One of the main common tenets of Monotheistic worships, is the inherent assertion, that there is only one God; that those who consider otherwise are wrong.
Hence, its a motivation that followers should make efforts to bring those who don't recognise their one God, under Him,because they are under the influence of wrong.
Hence, monotheistic religions all over the world, made the efforts to get more and more followers, and hence they got more and more followers.
Polytheistic religions, most often, did not see differences as problems, unless there were steep cultural disparities.
People with new Gods, meant , to polytheists, most often, new Gods to be worshipped and added to the pantheon.
Simple
history.stackexchange.com/users/4968/Rohit
It's odd no one has mentioned Judaism.
Arguably the source of both Christianity and Islam
, it has (despite occasional attempts) never been very imperialistic.
Also, Sikhism, another monotheistic religion, has not (that I know of) been particularly imperialistic.
On a slightly different topic, if members of two different monotheistic religions discover that they have no major doctrinal differences, can it be said that the religions are truly different?
Therefore, isn't it likely that multiple monotheistic religions have merged into just a few over the millennia, especially in the pre-Christian era?
history.stackexchange.com/users/12027/Dan
Not getting into the WHY.
But take a look at Egyptian religion and history.
They were polytheism ( http://en.wikipedia.org/wiki/Ancient_Egyptian_religion ) transformed into monotheism ( http://en.wikipedia.org/wiki/Atenism ) and then changed back.
Looking at those details and might provide some insight as to the how.
history.stackexchange.com/users/12023/Frank
Almost every religion or spiritual belief system in the world has at least some expression of a single god or an underlying force that permeates everything.
God in that sense is usually described as omnipresent, unchanging, eternal - that which has always been, always will be and from which everything is created.
For Hindus that would be Brahman , Christians would call that God , in Islam it's Allah , Taoism teaches of Tao and the list could go on.
Even in shamanic traditions there is almost always something that is recognized as the underlying force of all existence.
Modern physics has also observed and recognizes such a concept.
Physicists nowadays call it the Unified Field Theory .
In polytheistic belief systems the various gods are usually expressions of different aspects of existence.
Monotheistic religions speak of a direct connection that an individual can achieve with god.
Perhaps this makes the proposed final reward of monotheistic religions very appealing and the ultimate punishment very frightening.
Psychologically this is a far more powerful form of mind control.
Polytheistic religions don't speak of such grand rewards or punishments.
The different gods govern various aspects of the world and the believer is left to barter with the gods for good fortune.
history.stackexchange.com/users/12028/Herman Aus
If you look at the European area alone, there is a distinct shift towards a more 'modern' monotheistic religious in the rise of the Mystery cults in Greece and Rome.
Mithras, Sol Invictus, were somehow different and beyond and more exciting than the old pantheon.
Even in standard Paganism, individuals tended more and more to identify with a smaller set of gods as patrons - Jupiter and Hercules for Diocletian and the Tetrarchs.
Julian the Apostate's supposed return to Paganism was in a form that standard mythologies would find puzzling, as he imposed a single heirarchy for all pagan gods with one god at the top.
In the midst of this, Christianity gained traction as it also could offer a more personal, active relation between men and the gods than standard Paganism.
It won out in this case, but the other cases indicate that Paganism was becoming unsatisfying in general, and an opportunity for a new religion was open.
I would not consider Atenism a new religion, as it was a personal construction of one man and dropped when he died.
Even his son dropped it as soon as possible.
history.stackexchange.com/users/3116/Oldcat
In the world at the moment, the most popular religions seem to mostly be religions that worship only one "God", such as Christianity and Islam.  However, in the past there were many religions that worshipped a vast number of "Gods", such as Norse, Greek, Roman, Chinese etc.  Is there a historical reason why these older, multi deity relgions were replaced with religions that worshipped a singular god, and if so, when did this occur?
When and why did single deity religions become more popular than multi deity religions?
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<religion>
history.stackexchange.com/questions/21276
history.stackexchange.com/users/12014/Dr R Dizzle
A lot of mono deity religions were spread by wars and colonisation.  One reason why monotheistic religions grews could be due to military conquest as Christian and Islamic kingdoms expanded and spread their religion accordingly. The spread of Islam could also well be linked to the spice routes.
One possible reason why monotheistic religions grew in popularity was because their spread was linked to military conquest. The spread of Islam could also be related to the spice routes.