Also by Clarke, also set in the far future and also told twice: Against the Fall of Night / The City and the Stars.
For a change of pace: Ideocracy
John C. Wright’s Golden Age trilogy is set in a barely-recognizable far future of nanomachines and extensive neurological manipulation.
Greg Egan’s Diaspora ranges from some time in the 30th century to billions (and perhaps trillions) of years in our future (staying surprisingly hard sci-fi throughout). It starts out with a humanity having fractured into three different groups, fleshers, who are the most similar to ancestral humanity, gleisner robots, consciousnesses in robotic bodies, and the citizens, consciousnesses dwelling in a simulated virtual environment. Most of the novel is told from the point of view of the citizens.
I’m sorry, but I have to point out that a) this movie is only set 500 years in the future, b) everyone in it is eminently human and, most importantly, c) you spelled the name wrong. 
In Bruce Sterling’s Shaper/Mechanist universe – not set all that far in the future – both factions could be considered posthuman.
All Tomorrows: A Billion Year Chronicle of the Myriad Species and Varying Fortunes of Man by Nemo Ramjet.
It’s not so much a story as a futuristic documentary/history with a bunch of weird art. Lots of speculative evolution ranging from feasible to outlandish to body horror and nightmare fuel. It’s similar to Man After Man.
Premise: Future human civilization is destroyed by the Qu, an ancient race of aliens with mastery over genetics and nanotechnology. Instead of wiping out humanity completely they cruelly change us into different forms as punishment for resisting. When they leave our galaxy their grotesque human experiments start evolving independently across the different worlds. Some human races eventually reestablish their own civilizations and meet each other. Sometimes there’s peace, usually war.
Some of the more creative ones are the Modular People, which are individuals made up of dozens of body segments, each one its own intelligence. The Asymmetric People evolved on high gravity planets and look like a cubist painting or something from Lovecraft. The Asteromorphs are the only descendants of the original humans. They escaped the Qu by boarding generation ships and hiding in the voids between stars. To survive in space the human body was totally reworked. Now they look like a cross between grays, bats, and insects.
Unfortunately, I’m not sure if he ever got a publisher. I don’t see it anywhere on Amazon. It’s hosted on his official site, though.
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The same can be said about Egan’s Schild’s Ladder and Incandescence; his “Distress” is pretty near future, but post-humanism is happening as the novel progresses.
Robert Reed’s “Sister Alice” is very far future and post-human. So is Reynold’s “House of Suns”.
I second Alastair Reynolds’ House of Suns. So far in the future no-one really remembers who built the ruins the people are living on. Pushing Ice starts in the relatively near future but ends up thousands of years from now.
Stephen Baxter’s Manifold:Time travels further into the future than almost any other story, to a time when the stars have all gone out; his Xeelee Sequence travels far into a quite different future.
And those stories are very good.
Walter Jon Williams short story “Dinosaurs” also has post-human descendants of humanity.
You could think of the native races of the Ringworld as post-human in a way. In Niven’s universe, humans themselves are just Pak who never move past the “adult” stage but age and die in that stage for lack of…ugh, whatever that plant was that Pak need to advance to the Protector stage. The Ringworld’s denizens are of similar origins, and sufficiently speciated that crossbreeding is no longer possible (and of course Niven had to make up a word for that interspecies humping, because he is weird).
I came in this thread to mention Stapleton, only to see him in the very first response. 
Sticking with Niven, A World Out Of Time deals with Earth 3 million years into the future. (Time dilation/black hole ergosphere time wonkery is involved) The humans are more human that you’d have thought. Non-Known Space novel. Maybe throw the humans who live in The Smoke Ring universe too?
The humans in Alastair Reynolds’s Revelation Space series, and other stories set in that universe, are often decidedly post-human. (It’s a different series than either Pushing Ice, or House of Suns, both mentioned earlier in the thread.) Digitized personalities play a role in some stories, body modification is prevalent, as is direct genetic manipulation to emphasize one trait or another. The stories are set anywhere from a few years in the future, in the Solar System, particularly Mars and Europa, to several hundred years in the future in mostly local star systems (Episilon Eridani, Delta Pavonis)