The course, Payne's Valley, is named after three-time major victor Payne Stewart.
Tiger Woods took his first swings in public on Tuesday but did not reveal a timeline for his return to golf.
The site of the course will be Big Cedar Lodge in Ridgedale.
Stewart's wife Tracey says she's touched by the naming of this new course.
"[The Masters] probably wouldn't have been the best place for Tiger to start the year out after this most recent setback, and I think we should probably look, maybe something just after The Players Championship", he said during a recent appearance on The Rich Eisen Show. "Tiger and I were talking today as we were driving around". The real announcement of course, a new golf course.
"The back is progressing", he said.
The course will bear Payne Stewart's name.
The 41-year old Woods was then cheered on as he hit just wedge shots into a stunning par-three laid out in front of a steep cliff face and waterfall.
However, the first shot brought up flashbacks of Woods finding the pond three straight times from 103 yards at Congressional Country Club during last year's Quicken Loans National media day. Payne's Valley in Branson, Mo., is slated to open in 2019. Woods answered, "I was never opposed to that".
"But I grew up playing public golf".
The golf course development has kept Woods busy as he recovers from back surgery. We didn't have a whole lot of money and that's where I learned how to play.
Morris' Big Cedar Lodge stable of courses already includes Buffalo Ridge, a Tom Fazio design which hosts the Bass Pro Legends of Golf Champions Tour event this weekend and Top of the Rock, a nine-hole par-3 course designed by Jack Nicklaus, plus a 16-hole practice facility designed by the late Arnold Palmer.