Jealousy is the most common worry. The goal is not to surpress jealousy, but to understand it better in a poly relationship. Treat it more as an indication of what is going on and treat the issue and not the symptom.
For example, in a standard monogamous relationship, the guy may look at a girlie magazine and his wife catches him. She feels jealous and demands he stops looking at them because shs should be enough woman for him. But that is just treating the symptom. What she feels is insecure that her husband is not seeing her as sexy. If they address that issue, then him looking at porn is not such a big deal anymore.
Likewise, in a poly relationship, jealousy is a lot about insecurity or envy. Probably the biggest issue is worring about losing a partner to another or feeling less desirable. So for example, your boyfriend may worry that you like your older boyfriend better or will eventually just want to be with him. So you have to be clear that you still really want to be with him. Let him know that your feelings of love for this other guy does not diminish your love for him.
The biggest key to a polyamory relationship is communications. Everyone needs to get their feelings and desires heard and addressed. Find comfortable boundaries, but be willing to change rules over time as people adjust. There may need to be a slow period until people get more comfortable. Also think about how you would feel seeing your boyfriend with another woman. Imagine situations as they may arise and try to understand your feelings.
You should tell your boyfriend as soon as possible. If you wait, you will destroy a lot of trust and may create resentment. It will not be easy because our society teaches that monogamy is what we should strive for as oppose to an option that some people will want.