Bring a large pot of salted water to a boil and cook the spaghetti according to the package directions until al dente; drain and set aside.
Heat a large nonstick skillet over medium-high heat. Add the ground beef and cook, breaking it up with a spoon, until no longer pink, about 5–7 minutes. Drain any excess fat.
Sprinkle the taco seasoning over the cooked beef and add 2/3 cup water. Cook over medium-high heat, stirring, for 2–3 minutes until the seasoning is incorporated.
Stir in the tomato paste, undrained Rotel tomatoes, and condensed cream of chicken soup. Add the cubed Velveeta and shredded cheddar, then cook over medium heat, stirring frequently, until the cheeses are fully melted and the sauce is smooth.
Add the cooked spaghetti and rinsed, drained black beans to the skillet. Stir gently to combine and heat through, about 1–2 minutes.
Sprinkle with chopped cilantro if using, then serve immediately.