First, are you sure that's what you did? 403b plans can only be offered by non-profits. It would be very unusual for the same company to have a 401k and a 403b.
Second, if you got a 1099-R from the 403b, one of the first questions after entering the 1099 is "did you rollover these funds to another qualified account?" You should answer Yes, and the withdrawal won't be taxable. (Note that you must complete the rollover within 60 days or it doesn't count.)
