In Daniel 7:27 it says “Then the sovereignty, power and greatness of the
kingdoms under the whole heaven will be handed over to the saints, the
people of the most high. My question is in what way were the sovereignty,
power and greatness of the those kingdoms handed over to saints?

Being somewhat prideful, I do not find it easy to admit it
when I am not sure of the answer to a question, but I am afraid that is
the case here. Nevertheless, I have a couple of ideas for you to consider.

First, I see this passage being fulfilled, at least partially,
in the church: the kingdom of God on the earth. One of the main messages
of Daniel is that God will establish the saints and the kingdom forever.
God will destroy the persecutors of the Jews, and later of the
Christians. The kingdoms of Babylon, Persia, Greece and Rome are long
gone, yet the kingdom of God is alive and well. The kingdoms of this
world may think that they have sovereignty over the disciples of Jesus,
but our ultimate loyalty is to the king in heaven. We have the power of
an indestructible life. We have the greatness of being sons of God and
brothers with Jesus Christ.

Some would say that the prophecy you quote was fulfilled in
the edict of toleration under Emperor Constantine in the fourth century AD
and the subsequent rise to political and religious power and authority of
the early church. This event led to the suppression of the pagan
religions throughout the Mediterranean world. This is a possibility, but
as I see it, by the fourth century AD, the Roman church was already moving
toward apostasy, and the rise to political power of the church did more
harm than good to the spiritual life of the saints.

Second, the passage in Daniel seven finds its ultimate
fulfillment in the New Earth (Revelation 21). In heaven, the saints will
live with God forever. The saints will have amazing sovereignty, power
and authority in the future kingdom of God in heaven. This will be a
power and sovereignty which will far outweigh that of any earthly kingdom
that ever has or ever will exist.

In summary, God, through Daniel, may be referring to one of
the two aspects of the Kingdom of God mentioned above, but in my opinion,
Daniel seven is a reference to both.

John Oakes