Heat the olive oil in a large pot over medium heat. Add the onion and bell pepper; cook and stir until the vegetables are tender, about 5 minutes. Stir in the garlic, oregano, thyme, cayenne pepper, and bay leaves; cook for 1 minute.
Pour in the chicken broth and bring to a boil. Stir in the rice; reduce heat to low and simmer for 20 minutes.
Stir in the diced tomatoes with juice and sausage slices; simmer for an additional 10 minutes or until the rice is tender.
Remove from heat and discard bay leaves before serving.