The deal, which will be completed once international clearance is received, sees him move from Dean Court back to his native Holland until the end of the season.
The 30-year-old signed from Utrecht in the summer but made just two appearances during a short injury-hit spell with the Cherries, the last coming back in October under previous boss Paul Groves.
"We have quality players in that position and Frank has found it difficult to get a chance to stake his claim," manager Eddie Howe told the Daily Echo. "Due to the form of those players, he has been short of match time.
"We have watched him in training and in reserve games and don't feel he has warranted a place ahead of the other strikers.
"With the age that Frank is, I think he has to take that into account as well. He wants to play football and I can understand that."
Roda JC currently lie 16th in the Dutch top flight, and Demouge should be eligible for selection to face Heracles this Saturday.