Most 401(k)s will accept custodian-to-custodian transfers from old 401(k)s. If your new employer has a 401(k) plan, you can usually rollover your old 401(k) into a new one, but you will need to check with your new employer to find out for sure.
Keep in mind that the choice of mutual funds and other investments in the new 401(k) might be totally different from the investment options that your old employer offered. This means that you might need to liquidate all of your positions in the old 401(k) and transfer the cash balance.
This is not a complicated process, however, and can be done by checking a box on a form or perhaps giving verbal instructions to the old custodian company over the phone. It could potentially be a bad time to liquidate and transfer, though, depending on the market at the time.
The new 401(k) may give you a DCA (dollar cost averaging) option that helps you buy shares at the overall best average price per share, theoretically. It is possible that they can hold some or all of the same funds and investments, and they will basically transfer them over to the new account with what’s called an “in-kind” transfer.
If you do not have the option to move old accounts into your new 401(k) for some reason, or if you find that the fees and investment options make it unappealing, you can easy start up your own Traditional IRA outside of work and roll your old 401(k) money into it.