How do you develop taste for healthier foods?

Fat-loss has been something I've struggled with for most of my life. I've never been over-weight (I'm at the weight I should be at right now) but I've struggled with getting healthy and fit by changing my diet, doing more exercise and dropping fat.

The biggest issue I've had is giving up TASTE. It's the only reason why changing my diet has been so difficult. How do you develop a taste for healthier foods in the place of junk food? How would you recommend eliminating junk food really?

I'm fearing for my health, mainly because my family health history is full of heart disease, cancer, diabetes (this is a big one...) the list goes on. I don't want my future self to know that she's cut years off her life-span because she loved the taste of brownies.