The Australian Open didn't really become one of the 4 majors that all the top players competed in until the early 1980's. In fact, the tournament wasn't even held in 1986 because of a reshuffling of the schedule that year. As with most tournaments on the ATP and WTA tours, they are held during a time of year that has the best weather. For the Australian Open, that means during the summer time in the southern hemisphere, so, late January/early February. If you go back far enough in the history of the Australian Open you'll see the dates for it being in December, so it's moved around on the calendar a little bit over the years before it finally settled into the same two weeks over the past 25 years or so.
As for the other majors - it's really the same reason. Paris has good weather in late May/early June. Wimbledon has - typically - the best weather for tennis in late June/early July. The US Open could really be played anytime from June through September but Wimbledon and the French Open already had the calendar during the earlier summer months so it's been played in late August.
Also keep in mind that the French-Wimbledon-US Open are three different surfaces so the tour tries to allow for some time in between each event for players to play in warm up tournaments on the respective surfaces to allow players to adjust.