Fibre-rich foods help keep you fuller for longer by:
1. Lowering energy consumption when compared to non-fibre-containing alternatives.
2. By lowering the amount of energy absorbed from foods consumed. 
Dietary fibers provide a wide range of physiological impacts and health advantages, including:
Satiety~ state of being completely satisfied from food
Satiation ~ the satisfaction of appetite during feeding that marks the end of eating
Because of their properties of adding bulk and producing viscosity, they are thought to have an impact on satiation and satiety. Meaning that dietary fibres do in fact keep you fuller for longer. 
A study was conducted to investigate the effectiveness of a new low-fat yogurt fortified with a new combination of milk protein and guar gum fiber. The aim of this study was to see if a new low-fat yogurt enhanced with protein (8 g/serving) and fiber (2.6–2.9 g/serving) could reduce appetite in the short term by filling you up more than a control yogurt.
When compared to non-enriched yoghurts (control), the test product caused a substantial 16% fall in appetite score and a significant reduction in subjective appetite (all ratings) in both experiments. The idea of creating a low-fat yogurt packed with milk proteins and guar gum fiber was to create a healthy, low-energy packed snack that might aid in hunger control in between meals. 
From previous studies carried out we can see that eating meals that are high in fibre does keep us fuller for longer. This can lead to fewer sugary snacks being eaten, particularly in the evening time. The World Health Organization (2006) recommends eating a healthy, balanced, low-energy dense diet, rich in fiber and minerals. Protein and fiber have been shown to be significant modulators of short-term appetite.
Brownlee, I., Chater, P., Pearson, J. and Wilcox, M., 2017. Dietary fibre and weight loss: Where are we now?
Slavin, J. and Green, H. (2007). Dietary fibre and satiety. Nutrition Bulletin,
Lluch, A., Hanet-Geisen, N., Salah, S., Salas-Salvadó, J., L’Heureux-Bouron, D. and Halford, J.C.G. (2010). Short-term appetite-reducing effects of a low-fat dairy product enriched with protein and fibre. Food Quality and Preference