Former Rangers player McInnes, 54, joined after leading Hearts to second place in the Scottish Premiership - eight points above Rangers.
Hearts would have been the first team other than Celtic or Rangers to win the Scottish title since Aberdeen in 1985, but lost 3-1 to Celtic on the final day of a momentous season for the Edinburgh club.
Rohl's move to Austria after less than eight months at the helm was announced earlier.
Rangers said McInnes would join with assistants Alan Archibald, Paul Sheerin and Craig Clark.
“The demands here are clear, and our supporters rightfully have high expectations. It is up to me, my staff and my players to meet those expectations, and have this club performing as it should," said McInnes in a statement.
