(a) Many Syrian people have been driven out of the country and the majority headed to Europe.
(b) Many Syrian people have been driven out of the country, the majority heading to Europe.
(c) Many Syrian people have been driven out of the country—the majority heading to Europe.
Examples (b) and (c) are slightly different. The interruption, the majority heading to Europe, is treated as a minor one in (b) but a major one in (c). Interruptions are set off by different punctuation signs according to how much the writer perceives the impact these interruptions have on the sentence.
Example (a) is short of a comma, which should be placed before the coordinating conjunction and.
When two independent clauses are joined by a coordinating conjunction, we place a comma before the coordinating conjunction.
Edit (as hinted by Apollyon)
Also, as this process is still on-going, is heading is more appropriate than headed.
My suggestion is as follows:
(a1) Many Syrian people have been driven out of the country, and the majority is heading to Europe.
Example (a) links the points expressed by its two independent clauses slightly closer than what (b) and (c) do with their sentence structures.