DVI-D to HDMI Result: - Digital Video Cable
The High Definition Multimedia Interface (HDMI) is backwards compatible with all digital DVI interfaces so for this situation you will need a DVI-D to HDMI Cable to connect these two devices.
Be aware, however, that DVI does not carry the Audio signals that HDMI would between HDMI devices so you will need to find another way to send the audio signals depending on the types of audio interfaces your devices are using.
We will not get into that here.
These are the cables you may need and some adapters you may find useful for your application.
DVI-D to HDMI Female
DVI-D Female to HDMI
DVI-D Female to HDMI Female