Eventually = finally; ultimately; after an unspecified period of time or an especially long delay: ‘Eventually the family left the house.’ ‘Her constant campaigning eventually got her the nomination.’
When you mean that something will be done at the appropriate time (remembering that other things have to be done first), use in due course: ‘The new computers will be distributed in due course.’ ‘You will be informed of the committee’s decision in due course.’
