Are you his dependency, dependendee or something else? What is this type of opposite word called? I believe it is not called antonym, as that would be independent.
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I'd say you are his/her support or supporter.
See here and scroll down to the "noun" section.
If someone depends on you and you have a legal obligation to protect, support or care for them and their interests, then you are their legal guardian. The person who depends on you is your ward or dependant.
An informal word for the person who you depend on is your rock.
1611, King James Bible, Matthew 16:18
1991, Robert Harling and Andrew Bergman, Soapdish, Paramount Pictures
Simple language ordinarily trumps oral frippery (cf. Hemingway's "poor Faulkner" comeback), as exemplified by the first part of this sentence, but... There, are, times. So, thusly..
Not necessarily the most general alternative, but sponsor is sometimes used.
The Medicis were Galileo's sponsors.
If the support is monetary and public, patron can also be used.
The Medicis were Galileo's patrons. The NEA was Billingham's patron.
If the support is 'active', then advocate can be appropriate.
The indigent depended upon his advocate to navigate the bureaucracy.