Accents are related to local linguistic habits mixing in a new environment. From An Introduction to Language by Fromkin, et. al.

Regional dialects tell us a great dal about how languages change... American English, for instance, can be traced to the people who first settled North America in the seventeenth and eighteenth centuries. The early settlers came from different parts of England, speaking different dialects, which resulted in regional dialect differences in the first colonies. (p 401)

The chapter continues to discuss the three major dialect areas (Northern, Midland, Southern) and how incoming immigrants and overseas education shaped the dialects. An example is the rhotic r, or the pronunciation of the "r" sound. Southern England dropped their r's before consonants and at the end of words in the early 18th century and the practice carried over to North America (think Boston). At the same time, wealthy families would send children to England for education where they would pick up the non-rhotic habits of London.

As time went on, people from northern England, an area that retained the rhotic r, immigrated, as did people from other areas - Germans/Dutch to Pennsylvania, Scandinavians to Minnesota, etc, and their speech patterns formed the American dialects.

Australian English has a similar history. A limited number of ports in Australia and a mainly English immigrant population meant that all the English dialects were merged together into a single Australian dialect. Fromkin notes:

Each seaport attracted the same cross-section of British dialects, a heterogeneous mixture of regional and social dialects from almost every county. In each seaport there developed, subsequently, the same linguistic end product: a uniquely different accent (but with a particular bias towards London English, since about one-third of the convict population was from the London Area). Across the Tasman in New Zealand, the same process took place, with the result that the Australian and New Zealand accents of today are very similar to one another.

For more information on accents, check out any introductory linguistics textbook (which is what Fromkin, et. al. is) or head over to /r/linguistics.