It is very likely than you will be able to roll over or transfer these amounts after you stop working for your current employer. To be sure, the 403(b) and 457 agreements should be checked to determine the events that result in eligibility for withdrawals from the plans.
Assuming you are eligible to make withdrawals from the plans, the amounts can be rolled over or transferred to an eligible retirement plan. Rollovers should be done as a direct rollover so as to avoid the 20% mandatory withholding tax.
Be sure to ask the current providers whether there would be any fees incurred for terminating the accounts, and if so, whether there are any circumstances under which the fees would be waived or reduced.
Most importantly, you may want to consider working with a competent retirement plans counselor to ensure the proper steps are taken. The retirement counselor would need copies of the 403(b) and 457 agreements in order to determine the options available under the plans. These can be obtained from the plan providers.
If your balance includes after-tax amounts, be sure to check out Rollovers Of After-Tax Assets May Change The Landscape Of Your IRA.
This question was answered by Denise Appleby