Yes Sir Al, this is exactly what you need for your 783 30-06.

The Remington Model 783 Long Action Caliber Magazine is a standard factory replacement magazine. This magazine is designed to fit Remington 783 models which are chambered in Long action cartridges. It is designed to hold 4 rounds of ammunition. It features a steel sleeve and a polymer base plate. It is made to Remington factory specifications and tolerances, using the same manufacturing and materials as the original equipment magazines, ensuring perfect fit and operation.
Specifications and Features:
Remington Model 783 Replacement Magazine 19523
Long Action Caliber Cartridges
4 Rounds
.270 Winchester/.30-06 Springfield
Steel Body
Polymer Base Plate
Matte Black Finish
*******Fits:
Remington ******783 Bolt Action Rifles chambered in .270 Winchester and ******.30-06 Springfield

Yes the long action is correct for the model 783 30-06