Getting into a majority of the top schools will allow you to get into Strategy Consulting. Schools that immediately come to mind include:
Harvard, Stanford, Darden, Sloan, Kellogg, and Wharton. And to a lesser extent Johnson and Michigan.
Year after year strategy consulting seems to be a top destination for graduates of these schools. There are a decent number of people who try to make the transition from IT consulting to strategy consulting. The question is less can you make the transition once you get into school, but rather can you get into the school.
If you have a GMAT 700+ and a 3.5 then that's a start, but you still have several other criteria to fill.