I started exercising in the mornings when I stopped letting my current opinions, preferences and beliefs about myself define who I was.
I used to think I was definitely "not a morning person", but then I realised there isn't really such a thing as a "morning person". I haven't got a dislike of mornings and getting up early hard-wired into my DNA, and so these preferences and characteristics are choices, or at the very least, things I can change. If I wanted to choose to enjoy that part of the day, then I could.
And so I did! I stopped believing that people who got up to exercise early were somehow fundamentally different to me, or just a different "type" of person. There was something about that way of behaving that appealed to me, so I thought I would try it for myself. I now exercise (go for a run outside) in the mornings before coming into work, and I absolutely love it. By mid-afternoon, I forget I've even exercised that day, which is a wonderful feeling, suddenly remembering that I've done my body and my health some good! Exercising first thing generally makes me feel happier, more confident during the day, more energetic and refreshed, and it makes me want to make healthier choices for the rest of the day.
Having said all of that waffle, this is just me, and these are just my views. I really do believe that there's very little about a person that they don't have the power to change, or at least be open to change, but I've nothing to base that on other than my own intuition and experience. You may entirely disagree, and there may well be something that makes it impossible for you to derive any pleasure from rising early to exercise, or you may simply not enjoy the exercise very much when you're giving it a real good shot. All of this is totally fine, and then it's just a case of finding other habits that you do find more pleasurable.
So responding to your question in a nutshell, I motivated myself to exercise early in the day by:
1. Abandoning the idea that my current preferences and feelings about this were set in stone (which in itself, I found very liberating), then, once I felt more open minded,
2. Just having a go at it, to see how it made me feel!
If I enjoy it, then these positive sensations motivate me to do it again and again. If I have a good try and I really don't enjoy it, then I stop. As I said before, I do believe that there's not much that I don't have the power to change about myself, but at the same time, why do you need to change everything anyway? Sometimes it's perfectly fine to just stay as you are. In this example, there are other forms of exercise, other times to exercise, and so on, so if one execise-related thing seems to be particularly difficult to enjoy, then I just move on and try something else. It's not the end of the world if you try and try, and really don't like getting up to exercise.
Sorry, that was a bit long!