From the Online Etymology Dictionary:
1471, "soft mass formed by chemical manipulation," from M.L. amalgama, "alloy of mercury (esp. with gold or silver)," an alchemists' word, perhaps an alt. of L. malagma "poultice, plaster," from Gk. malagma "softening substance," from malassein "to soften," from malakos "soft." The word may have come from Gk. via Ar. al-malgham. Amalgamation in the figurative sense of "combining into one uniform whole" is from 1775.
According to Microsoft Encarta, amalgam originally meant "soft alloy" in English, but it's easy to see how its use could quickly spread to mean "mixture", in any metaphorical sense.
Interesting to me, also, is the addition of a new noun form, amalgamation, in 1775, which seems to imply that the verb form should be amalgamate -- and 233,000 hits on a Google search for the latter is proof positive that the word is being used, at least. I've never heard amalgamate used by anyone, but it does sound natural as the verb form. Amalgamation appears to be used more often to describe mergers, in a more general sense, or the act that forms the merger.
Of course, any Greek assimilation of an Arabic term is interesting in its own right. I wonder what the event was that introduced this word to the Greeks?