McInnes will replace Craig Brown, who revealed last week that he will be moving into a director's role at Pittodrie.
It is reported that the former St Johnstone manager could be confirmed as the Dons' boss as early as Monday, with terms to be finalised.
Former Scotland manager Craig Levein had been linked to the post, while Ross County rejected an approach to open talks with Derek Adams.
McInnes joined Bristol City in 2011, after leading St Johnstone to First Division title success and promotion to the SPL.
But a run of poor results at Ashton Gate led to the former Rangers player being sacked in January after a 4-0 defeat by Leicester sent City to the bottom of the table.
Aberdeen sit just two points off the top half of the SPL table, despite having won just once in 11 games this year.