The company that holds your loan makes the decision to transfer servicing to another institution. The company does not have to ask your permission to transfer the servicing, but it does have to inform you of the transfer.
The transfer of servicing should not affect you or your mortgage adversely. 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 according to 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 time-frame, you should ask whether this agreement would be honored by the new lender.