Can you connect BH1790GLC and TMP117 sensors to an Arduino board?
Yes, the sensors will work with microcontroller(s). What you look for is the interface they use. In this case it is I2C interface. Be careful thou: You have to check voltage levels your microcontroller works with and selected sensor voltage level. Some of the Arduino works with 5V levels and some sensors may accept max of 3.3V or 4.5V on I2C pins. This is why you would need either:  


Choose 3V powered microcontroller
Use 5V powered microcontroller (like Arduino Uno) and voltage level converter  


Also worth to note that these two sensors would need some additional circuitry to work with your microcontroller. Before any commitment I would try to find a development board (a board with mentioned circuitry with easy to acces pins for providing necessary signals/voltages/ground/etc).
Good luck!