Steele has worked most recently at Manchester City as well as Aston Villa, Leeds and Derby among others and agreed to switch to Ewood Park after leaving Eastlands last month.
The former Newcastle player is Ince's third backroom appointment this week.
Rovers chairman John Williams said: "Eric comes with a lot of experience at the very highest level. We are delighted to have him on board.
"He clearly knows his stuff and it's fair to say he's been responsible in bringing Joe Hart through at Manchester City."