Chad Pennington's star quarterback son is following in his footsteps ... announcing that he's committed to Marshall University --- his father's alma mater!!!

Cole Pennington -- a 3-star junior QB at Sayre H.S. in Lexington, KY -- made the announcement Wednesday via Twitter ... saying he's stoked to join the Herd.

"To be a college student-athlete has always been a dream of mine," Cole says.

"Thank you, Coach Huff, Coach Cramsey, and the rest of the Marshall Football Staff for giving me this opportunity to say I'm 100% committed to Marshall University!!!! Go Herd!!!"

CP got interest from other schools like Akron, Ball State and Eastern Kentucky ... but come on, the dude is destined to take his talents to Huntington!!!