According to David Pearce, in 2015 Musk was ambivalent towards the idea of transhumanism.  When however in June 2016 he started advocating neural enhancement, it's fair to describe him as a de facto transhumanist.  He's also a transhumanist presentist. 
“By far you have more power, more capability, than the President of the United States had 30 years ago. If you have an Internet link you have an article of wisdom, you can communicate to millions of people, you can communicate to the rest of Earth instantly. I mean, these are magical powers that didn’t exist, not that long ago. So everyone is already superhuman, and a cyborg,” says Musk [at 33:56].
In 2016 he was invited to join Trump's economic advisory team. 
Musk's transhumanist tendencies appear to stem from a mixture of pragmatism and existential fear. Most of his post-PayPal ventures have focused on reducing the risks humans pose to themselves and the planet(s) we live on. Tesla and SolarCity became Musk projects out of his desire to reduce human reliance on polluting fossil fuels, SpaceX came out of a desire to have a "Plan B" in case Earth could no longer sustain humans by pushing humanity out into the solar system, and OpenAI came out of Musk's fears that the first creators of an Artificial General Intelligence might not use it in a way that benefits humanity. Neuralink doesn't fully fit this pattern, but it's probably Musk sees this as levelling the playing field with a future AI, or allowing eventual full consciousness transferrence onto digital media, effectively making the human species significantly more resilient.
"I'm not actually a huge proponent of longevity," Musk replied. "I do think that having a good life for longer is better — we want to address things that can happen to you when you're old, like dementia, that's important — but I don't know, I definitely don't want to live forever."
"How many years do you want to live?" Sorkin pressed. "About 100 good ones," Musk replied. "100 good ones, or 100 more good ones? You're 44.""100 good ones total," Musk said. "Well, maybe a little bit longer."