No, you will not receive a 1099-R from the company who receives the funds but rather from the company who distributes the funds to be rolled-over. This 1099-R will have a code G in box 7 to show that it is a rollover and box 2a should have a 0 showing none of the distribution as taxable. You will have to enter this information, because the rollover must be reported. But you will not pay tax.
You may receive a different form from the company that receives the funds, Form 5498. This may not happen until after the April 18 filing deadline. However, this form is informational only and only needs to be saved for your records. None of the information on the form will be reported for tax purposes. Here is a TurboTax webpage with more information:
What Is IRS Form 5498? - TurboTax Tax Tips & Videos
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