Securities brokers have a process called ACATS (Automated Customer Account Transfer Service) that is managed by the NSCC (National Securities Clearing Corporation) for moving open positions and cash from one broker to another. An ACATS transfer essentially takes your account from one broker and replicates it, including your open positions, with another broker.
Your old broker can charge you for initiating an ACATS process. Most of the time this fee is between $50-$100 per account. However, this may not be an issue at all. Keep in mind that your new broker wants your business. It is very likely that they will reimburse you for this expense but you have to ask for it. Don't hesitate to find out whether they will cover these costs for you.