There is no doupt that ancient Macedonians were Greek. It is thoroughly proved by historic documents and archaeological discoveries which can be found in history books and museums in Greece and arround the world. The most important archeological discovery in Macedonia is the tomb of King Philippos II. It was excavated in Vergina, Greece in 1978 and it proves beyond any doubt the Greekness of ancient Macedonia. All the findings are characteristic of the Greek culture and all the inscriptions are written using the Greek language. Among the discoveries of this tomb is the "Vergina sun" the symbol that FYROM attempted to use on its flag initially.

Some facts which prove that ancient Macedonians were Greek.

• Macedonians spoke a dialect of the Greek language
  All the monuments and inscriptions found in the Macedonia region are written in the Greek language.
  It is also crearly stated by the Latin historian Titus Livius :
  "Aetolians, Acarnanians, Macedonians, men of the same language..." (T. Livius XXXI,29, 15)
  and the Greek historian Herodotos :
  "Since they speak the same language, they should end their disputes by means of heralds or messengers..." (Herodotos, The histories 7.9.2)

• Macedonians had Greek names
  All the ancient Macedonian names mentioned in history or found on tombs are Greek. All the kings of Ancient Macedonia had Greek names. Nobody discovered ancient Macedonian names ending to -ov or -ovski or whatever.
  Alexander's name is Greek. The word "Alexandros" is produced from the prefix alex(=protector) and the word andros(=man) meaning "he who protects men". The prefix "alex" can be found in many Greek words today (alexiptoto=parachute, alexisfairo=bulletproof - all these words have the meaning of protetion).
  Philip's name is also Greek. It is produced from the prefix Philo(=friendly to something) and the word ippos(=horse) meaning the man who is friendly to horses. The prefix "philo" and the word "ippos" are also found in many words of Greek origin today (philosophy,philology, hippodrome,hippocampus).
  Some more ancient Macedonian names can be found here

• Macedonians fought together with the rest of the Greeks.
  Macedonians always fought along with the other Greek city-states against enemies from Asia.

• Macedonians took part in the Olympic games
  It is well known then ONLY Greeks were allowed to take part in the ancient Olympic games. The first Macedonian who took part in the Olympic games was Alexander I, King of Macedonia between 498-454 bc .

• Macedonians celebrated the same festivals as the rest of the Greeks.
  Examples of festivals which were celebrated in Macedonia as well as in other Greek states are the "Hetaireidia", the "Apellaia" and many more.

• Macedonians worshiped the same Gods as the rest of the Greeks
  Several temples dedicated to the Greek Gods have beem discovered in Macedonia and especially in Dion the religious center of ancient Macedonians. It is obvious that the Macedonias worshiped the 12 Olympian Gods as the rest of the Greeks The Gods were "living" on Mount Olympos which happens to be located in Macedonia. Would that be possible if there was hostility between Macedonians and Greeks? This is another proof that Macedonia was considered a part of Grrece.
  

• The regions of ancient Macedonia had Greek names
  The regions which formed ancient Macedonia had Greek names. Most of these names are used in Greece even today. You can see a list of the regions of ancient Macedonia here

• Macedonian architecture was similar to the Greek architecture
  All the buldings found in the Macedonia region have many common characteristics with the ones found in the rest of Greece. Palaces, temples, theaters markets are characteristic sampes of ancient Greek architecture.
  

Some more evidence from history

1. The famous ancient Greek play writer Euripidis wrote and originally presented most of his plays in Pella, the capital of Macedonia. How was that possible if the audiance spoke a different language?

2. After the battle of the Grannikos Alexander the Great sent to Athens some pieces of armor captured from the Persians with the following inscription :
"Alexander, son of Philip and the Hellenes, except the Lakedaimonians, offer these spoils taken from the barbarians of Asia".

3. Macedonia was a member of the Delphic Amfictiony , an institution which was open only to Greeks

4. When Alexander arrived in Asia he visited the ancient Greek town of Troy (Troia), where he sacrifised to the Greek Gods to help him in his quest.

A part from the "Treaty of Alliance" between king Philip V of Macedonia and Hannibal.

"This is a sworn treaty made between us, Hannibal the general, Mago, Myrkan, Barmokar and all other Carthaginian senators present with him, and all Carthaginians serving under him, on the one side, and Xenophanes the Athenian, son of Kleomachos, the envoy whom King Philip, son of Demetrios, sent to us on behalf of himself, and the Macedonians and allies, on the other side. `In the presence of Zeus, Hera and Apollon; in the presence of the Genius of Carthage; ...and in the presence of all the gods who possess Carthage; and in the presence of all the Gods who possess Macedonia and the rest of Hellas; and in the presence of all the gods of the army who preside over this oath. Thus said Hannibal the general and all the Carthaginian senators along with him and the Carthaginian soldiers: ...That King Philip and the Macedonians and the rest of the Hellenes. . .
(Polybios 7.9.1-7)

Alexander's speech to his solders one year before his death

I wish all of you, now that the wars are coming to an end, to live happily in peace. All mortals from now on shall live like one people, united, and peacefully working towards a common prosperity. You should regard the whole world as your country, a country where the best govern, with common laws, and no racial distinctions. I do not separate people, as many narrow-minded others do, into Hellenes and barbarians. I am not interested in the origin or race of citizens, I only distinguish them on the basis of their virtue. For me, each foreigner is a Hellene, and each bad Hellene is a barbarian. If ever there appear differences among you, you must not resolve them by taking to arms; you should resolve them in peace. If need be, I shall act as your negotiator.

The speech of Alexander I when he was admitted to the Olympic games

"Men of Athens... Had I not greatly at heart the common welfare of Hellas I should not have come to tell you; but I am myself Hellene by descent, and I would not willingly see Hellas exchange freedom for slavery.... If you prosper in this war, forget not to do something for my freedom; consider the risk I have run, out of zeal for the Hellenic cause, to acquaint you with what Mardonius intends, and to save you from being surprised by the barbarians. I am Alexander of Macedon."
(Herodotus, The Histories, 9.45)

What was the origin of ancient Macedonians?

"The name of the ancient Macedonians is derived from Macedon, who was the grandchild of Deukalion, the father of all Greeks. This we may infer from Hesiod's genealogy. It may be proven that Macedonians spoke Greek since Macedon, the ancestor of Macedonians, was a brother of Magnes, the ancestor of Thessalians, who spoke Greek."
(Professor N G L Hammond, University of Cambridge, UK, 1993)

" This was Macedonia in the strict sense, the land where settled immigrands of Greek stock later to be called Macedonians"
(Professor W J Woodhouse, University of Sydney, Australia, 1917)