Hi newcomer and welcome to the Tom's hardware forum.
Yeah, the Phenom II processors can works in Phenom mobos, but in some cases needs update the BIOS of the mobo. Bear in mind that not all the Phenom II can works in Phenom mobos.
That specific processor that you post the link is supported by the mobo that you want, and according to the ASUS's web site you don't need update the BIOS.
You can see the CPU support list of your mobo here
are the specifications of your processor, that in newegg is HDX945FBGIBOX, but is you see is the same HDX945FBK4DGI, that is the 1st X4 945 in the list.