Pre-emptive multitasking OS's on the big boxes have been around for a very long time, and were sometimes also referred to as "time sharing" systems. The first programming job I ever had (in 1976) was on a proprietary OS that the company I worked for developed, and it did pre-emptive multitasking. Basically all pre-emptive multitasking OS's use a time-slicing model, with individual users yielding the remainder of their slices at any time that they need to wait on a system resource, such as an I/O to be completed.
The Amiga was the first home computer with pre-emptive multitasking though. The Lisa and the early Mac would allow you to have several tasks going at the same time, but only one could be active at the same time, and the OS wasn't capable of automagically switching back and forth between them. The Amiga's OS has much in common with Unix, and I'd be very surprised if Unix didn't influence the Amiga OS design, with the goal being to provide the best Unix features with a smaller set of hardware requirements. They succeeded brilliantly at that, IMHO.