I've struggled with motivation during stronger bouts of depression, myself. In the last few months, I think I have gotten myself figured out, though. For me, I think key ingredient #1 is music. I do a fair amount of dancing and exercises that I can do to a beat, so finding the right music was huge. Now, I didn't like Run DMC when I was a kid and they were popular, but I do now, at least for exercising. I'm adding to my playlist all the time, and have found that it's either the "get up and dance" or "fight" music that gets me the most motivated. Typically, even if I don't want to exercise, if I start the playlist, I will start moving.
I also have zero attention span, so I rarely dwell on anything for very long. What I do instead is do one exercise for 30-60 seconds or so and then change. I'll usually come back to the first one later. I found that spending too long on any one movement just ended up making me feel bored and like I was getting ready for drudgery when it was time to get going. The dreadful feeling of impending intense, long work would often cause me to have second thoughts about my workout. Hopping back and forth from squats to windmills while pumping up the jam is a thought that is a lot more energizing for me. It's like I'm going to a party instead of physical therapy.
There are some specific exercises that I really have to do because of some joint problems. Of course, again, these are boring, so I try to position them in between dance party moves, so I feel like I am getting a Scooby Snack afterwards.
When all else fails, and not even Bust a Move is getting a reaction, mild stretching often seems to kick my body into "active" mode. I don't know the science but I do know that when my muscles start engaging, a lot of times they seem to want to keep going. I find that a little stretching is a lot less offensive idea than some of my more involved non-routine routines, being gentler and less energetic. Nevertheless, those stretches can be a good starting line.
These days, it seems like I have very little trouble getting my exercise going, but it's basically fun for me and that really, really helps. Ultimately, exercising has improved my depression by a tremendous amount, but only if I get and keep my heart rate up for a while. I could walk all day long and battle with depression all evening. I'd say that in the last nine months of really consistent, regular heart-pumping exercise (one hour for four days a week and a half-hour for three), my bouts of severe depression have probably diminished by about 80%. I've gained a lot of muscle, too, and that makes me feel more like a badass, which helps my anxiety. I hope you find a solution that works for you. I think consistent exercise has been one of the best things on the planet for me, but I have hypermobility syndrome, too, and it has vastly improved that situation, as well.