It was developed by a team led by John Couleur out of work they had done for the military MISTRAM project in 1959. MISTRAM was a tracking system that was used on a number of projects (including Apollo) and the Air Force required a data-collection computer to be installed in a tracking station downrange from Cape Canaveral. The data would eventually be shared with the 36-bit IBM 7094 machine at the Cape, so the computer would likely have to be 36-bits as well (why they didn't use an IBM 7094 is something of a mystery). GE built a machine called the M236 for the task, and as a result of the 36-bit needs, it ended up acting a lot like the 7094.
GE originally hadn't intended on entering the commercial computer market with the machine. However by the early 1960s GE was the largest user of IBM mainframes, and purchasing their own machines seemed like an excellent way to lower the costs of their computing department. In one estimate the cost of development would be paid for in a single year of IBM rental fees. Many remained skeptical, but after some internal wrangling, the project to commerciallize the M236 eventually got the go-ahead in 1963.
The 600 series used 36-bit words and 18-bit addresses. It supported floating point in both 36-bit single-precision and 2 x 36-bit double precision. It also included a number of DMA processors for handling I/O. The CPU could hand off short programs (rather simplified) to the DMA channels, which would then process the data to or from the memory, and raise an interrupt when they completed. This allowed the main CPU to move on to other tasks while waiting for the slow I/O to complete, a primary feature of time sharing systems.
The machine was originally offered as the main GE-635, and the half-speed GE-625. In fact both machines had identical core CPUs, but the 635 had two of them, in what is likely the first example of a general purpose SMP system. Apparently an even smaller GE-615 was offered, but it is unclear if this actually existed.
However continuing problems with the reliability of the magnetic tape systems used with the system cast a pall over the entire project. In 1966 GE froze many orders while others were cancelled outright. By 1967 these problems were cleared up, and the machines were re-launched along with an upgraded version of the GECOS operating system.
In 1965 work started on the Multics project, and GE was selected as the computer supplier. They saw this as an opportunity to clearly separate themselves from other vendors by offering this advanced OS which would run best only on their machines. Multics required a number of additional features in the CPU to be truly effective, and John Couleur was joined by Edward Glaser at MIT to make the required modifications. The result was the GE-645, which included a number of security levels in the CPU, and instructions for handling virtual memory.
A follow-on project to create a next-generation 645 started in 1967. The new GE-655 replaced the individual transistors from the earlier models with integrated circuits, which about doubled the performance of the machine while also greatly reducing assembly costs. However the machine was still in development in 1969, by which time the Multics project had ground to a halt.
GE then decided to sell their entire computer division to Honeywell in 1970, who renamed the now working GE-655 as entire line as the Honeywell 6000 series. The 655 was eventually officially released in 1973 as the Honeywell 6080 and they sold a total of about a dozen machines. Various smaller versions were offered as the 6070 all the way down to the 6030. A version of the 6080 with the various Multics-related changes similar to the 645 was released as the 6180. Later versions (mostly re-packaging) were released under a series of seemingly random names.