But ancient Greek city-states, who spent more than a decade fighting against Alexander's father Philip II of Macedon, were probably less enthusiastic.
A skilled general and diplomat who transformed Macedon -- ancient Macedonia -- from a tribal backwater into a regional superpower, Philip waged a sustained campaign against the Greek city-states, eventually crushing Athens and Thebes at the Battle of Chaeronea in 338 BCE.
For the first time in history, most of the Greek mainland was then under the influence of a single ruler, ending decades of internecine warfare.
"Philip was a rather unscrupulous ruler, who tried to, and finally managed, to expand Macedonian power over the rest of Greece... of course, there was a lot of antagonism against him," said Reinhard Senff, scientific director of the German Archaeological Institute in Athens.
At the time, many Greeks did not consider the Macedonians part of the Hellenic tradition -- even though they spoke Greek and worshipped the same gods.
However, in contrast to many of the city-state democracies, Macedon was a monarchy.
The question of ancient Macedonia's Greek heritage has been thrust into the spotlight recently as modern-day Greece and Macedonia, a former Yugoslav province, attempt to settle a 27-year dispute over the right to the name.
Zenith of Greek influence
The greatest orator of the era, Demosthenes of Athens, penned fiery speeches against Philip, calling him a "barbarian".
"Force of habit," said Stephen Miller, professor emeritus at the University of California, Berkeley.
"For Demosthenes, anyone who disagreed with him was a 'barbarian'. He called some of his fellow Athenians barbarians."
In one of the most striking acts of his reign, Alexander razed the leading city of Thebes to the ground after subduing a revolt.
Yet the ancient Macedonians held Greek culture and education in high regard.
Alexander was an avid fan of Homer's Iliad, and Philip enlisted the famed Athenian-trained philosopher Aristotle to tutor his young heir.
"The royal court in Macedon, from the fifth century onwards, very much cultivated Greekness... they esteemed Greek culture and education," Senff said.
As with past Macedonian kings, Philip also participated at the Olympic Games, a competition exclusively reserved to Greeks.
Horses owned by the king won at three successive Games, and Philip later dedicated an imposing monument bearing his name, the Philippeion, to Zeus at Olympia.
"We can say that the (Greek) origin of the Macedonian kings was widely accepted already in the fifth century BCE," said Miller.
But whereas the Macedonian royal family was acknowledged to be descended from the mythical Greek hero Hercules, their subjects were treated differently by the Greeks.
"The Macedonians were not considered Greeks by the Greeks... as far as we know until the end of the classical period only the royal family was admitted to Olympia," said Senff, who heads excavation work at the birthplace of the Olympics.
Alexander's conquests marked the zenith of Greek cultural influence and power in east and central Asia and north Africa.
After his death, successor states continued to operate in what is now Egypt, Turkey, Syria, Afghanistan and India.
This period, known as the Hellenistic era, lasted nearly 300 years until the rise of Rome.
The Romans later created an enormous province called Macedonia that included parts of modern-day Albania, Macedonia and Bulgaria.
Slavs subsequently migrated to the area of present-day Macedonia from the 6th century AD onwards.
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