The IRS says that you can roll a 403(b) plan into a 401(k) plan if you now work for an employer that offers a 401(k). You can also roll a 403(b) plan into a solo or independent 401(k) plan if you are self-employed.
However, if you work for an employer that does not offer a 401(k) plan, then you cannot roll a 403(b) plan into any type of 401(k) plan. If your employer offers a SEP plan or 457 plan, then you can also roll a 403(b) plan into one of those.
It also works the other way: If you had a 401(k) at the old job, and the new employer only offers a 403(b), you can roll over the money too.
Of course, you can always roll a 403(b) or other qualified plan offered by a previous employer into a traditional or Roth IRA. Current rules allow you to then roll that money over into a 401(k) plan if you are hired by an employer that offers this plan in the future, as long as the money from the 403(b) plan has not been commingled with contributory funds that you deposited into the IRA.
One caveat: While the IRS regulations allow rollovers of assets between 401(k) plans and 403(b) plans, employers are not required to allow rollovers into the plans they maintain. Whichever transfer you’re thinking of, your employer must permit it. Happily, most employers do; the more assets in their plans, the better, is their general thinking.
For more, see Common IRA Rollover Mistakes.