The transfer of your mortgage servicing will have no effect on you or your mortgage. The original terms and conditions of your mortgage will stay the same. Your interest rate and duration of your loan will not change on fixed rate loans. Your payment should stay the same or on the same schedule except in cases where changes in taxes or insurance requirements increase or decrease the escrow amount.
If you have an adjustable rate mortgage (ARM), the original conditions of the mortgage contract stay in effect and the rate will change per the adjustment periods (i.e. every six months, annually, every three years, etc). This information is contained in your contract, but you are welcome to verify the information with your new servicer.
If your original lender agreed to let you refinance to a fixed-rate mortgage within a certain timeframe, you should ask whether this agreement would be honored by the new lender. The company/investor that holds your loan makes the decision to transfer servicing rights to another mortgage servicer.
The company does not have to ask your permission to transfer the mortgage servicing rights, but the company/investor is required to inform you of the transfer.