There are currently two different accounts of the history of the whiteboard, one from the US and one from the UK and both dating to the late 50's early 60's.

The first version has the white board invented by Martin Heit, a photographer and Korean war veteran. The idea was originally developed for having next to a wall phone to take messages down on. During his work with film, he realized that notes could be recorded on film negatives using a marker pen and could be easily wiped off with a damp tissue. Early whiteboards were made out of film laminate, the same glossy finish found on film negatives. Additional advertisements and dated documents are will be made available online soon.
 

Original early 1960's ad for "Plasti-slate" the first whiteboard/dry erase board invented by Martin Heit

A prototype was made and ready to be revealed, when the showcase at the Chicago Merchandise Mart burned down the night previous to its unveiling. Mr. Heit chose to sell the patents to the company that would eventually become Dri-Mark, who began to introduce them into the education world.

The second account is that Albert Stallion invented the whiteboards while working at American steel producer Alliance in the 1960s. This can be verified by meeting minutes of Alliance, although these are not in the public domain, and by confirmation by Mr Bill Smit of Smit Visual Supplies BV, who was present at the meeting in question. This account of the history of the whiteboard is as follows:

One of the products Alliance produced was enameled steel, which was highly scratch resistant and easy to clean. It was used for architectural cladding purposes. One day Mr Stallion commented in a board meeting that this product would be a good addition in the market of writing boards, to replace the traditional chalk board in use until that time. His comments were not taken very seriously and being the entrepreneur he was he left the company and started his own company, Magiboards, selling enamel steel whiteboards.

It took a while before these boards started to really be accepted, not least because the initial boards were wet wipe, as there were no dry markers, but in the 70's marker manufacturers soon saw the potential of such markers and dry wipe whiteboards started to be accepted more readily.

The first whiteboards were very expensive and were made of an enameled steel. Cheaper alternatives since made their way into the market, including laminated chipboard, high pressure laminates and steel boards with a white, usually polyester or acrylic, coating. Enameled whiteboards, also referred to as porcelain, or sometimes even glass boards, remain the highest quality boards available though, since the alternatives all have a tendency to leave residue of erased markings on and in the surface and are difficult to keep clean after a short while. Hard baked vitreous enamel is so non-porous that marker ink does not penetrate the surface and these board remain erasable for ever if not scratched. Due to the price difference the cheaper alternatives now have the largest market share in the office products market, but in more demanding environments, such as schools, universities, etc. porcelain boards remain the gold standard.

In the mid-1960s, the first whiteboards began to appear on the market. In classrooms, their widespread adoption did not occur until the early 1990s when concern over allergies and other potential health risks posed by chalk dust prompted the replacement of many blackboards with whiteboards.