If you're looking for something exactly like IOCP, you won't find it, because it doesn't exist.
Windows uses a notify on completion model (hence I/O Completion Ports). You start some operation asynchronously, and receive a notification when that operation has completed.
Linux applications (and most other Unix-alikes) generally use a notify on ready model. You receive a notification that the socket can be read from or written to without blocking. Then, you do the I/O operation, which will not block.
With this model, you don't need asynchronous I/O. The data is immediately copied into / out of the socket buffer.
The programming model for this is kind of tricky, which is why there are abstraction libraries like libevent. It provides a simpler programming model, and abstracts away the implementation differences between the supported operating systems.
There is a notify on ready model in Windows as well (select or WSAWaitForMultipleEvents), which you may have looked at before. It can't scale to large numbers of sockets, so it's not suitable for high-performance network applications.
Don't let that put you off - Windows and Linux are completely different operating systems. Something that doesn't scale well on one system may work very well on the other. This approach actually works very well on Linux, with performance comparable to IOCP on Windows.