You'll be able to join a consulting firm straight from university if you're graduating in Engineering. Consultancies hire from a wide range of disciplines, you don't have to have done Economics or Management to get in. The most common disciplines they look for are degree courses with a numerical angle (so engineering, maths, economics, etc.); foreign language fluency is also highly sought by many firms.
If you don't want to go straight into consulting upon graduation for some reason, then yes the most common route thereafter would be to do an MBA at a top school and for that to then be your stepping stone for a move into consulting.