I cannot believe nobody has recommended David Zindell yet! His work is a masterpiece of transhumanist fiction.

His Requiem for Homo Sapiens series is preceded by a short story Shanidar, you should read it first to get a taste of what's next. If you want more, then the next four books are:

• Neverness
• The Broken God (My personal favorite)
• The Wild (IMHO the worst of the series, but Nikolos Daru Ede is just lovable)
• War in Heaven

I'll second After Life, it's very short but definitely one of my favorite pieces of h+ fiction. The work of Cordwainer Smith (He only wrote a novel and a few short stories) could also be considered transhumanist fiction, as it includes genetically-engineered super-furries.

Sirius, by Olaf Stapledon, is also a very, very good (And rather depressing) novel about an uplifted dog. In the short story deparment, my personal favorite (Even better than Shanidar) is Fermi's Urbex Paradox, a real must-read about a posthuman who travels around the galaxy investigating the remains of civilizations and provides an answer for the Fermi Paradox. Crystal Nights, by Greg Egan, is also good.

Full list