We did this when we switched from formula to cow's milk, as Amy didn't take kindly to that at all lol.My children's pediatrician (and my mom) always suggested mixing the formulas together and making it a gradual transition.
*Start with 3/4 current formula, 1/4 new formula
*After a day, do 1/2 current, 1/2 new
*Then move to 1/4 current, 3/4 new
*All new formula
Took us about a week. We switched from milk-based formula (Enfamil) to Isomil Soy with our daughter. We also switched from Isomil to Alimentum with our son.
Worked great for both kids. Good luck!