What is the best way to transition into a career in business?

If you did a solid EE degree (good gpa, strong school) and you have decent verbal skills – written, oral, you can transition immediately to the business world, particularly consulting and operations management.
 
A hybrid role: ops management in technical field can get you exposure to management teams very quickly. Few business people have technical expertise. A technical person who can learn the mechanisms of business is always valuable. If you want to go the consulting route, and you’re aiming for a top tier firm, cement your expertise  before you beat on their doors. It doesn’t take long to cement a modicum of expertise – you won’t be a master, but you’ll be able to talk well above your years in as few as 9 months of serious work. But do the serious technical work, not project management. At a top tier consulting firm they will value you for your raw *intellectual* power.
 
It’s kind of a sham, but engineers have gotten away with that gambit for years. You can too.
 
MBA, not yet. Build your EE-field expertise + transition to consulting or head into ops management. After a few more years of work (3-4years) then consider bschool. MBA is a launching pad. Much of the knowledge gained can be accessed freely in books. You don’t go for the classes and book-learning. You go to position yourself for launch. It helps to be very clear about what and how you will launch. Otherwise bschool is an expensive 2 year party.
 
*Please note, I’m talking about 2-year full time programs and focused on the handful of internationally credible MBA programs. I am also assuming you are interested in a competitive career trajectory, not toiling as overhead.
 
**Also note, I did not acknowledge the MIM. Value prop is not there.