In a word, yes. However, we suggest that you should seek your own legal opinion before relying on the information below.
In Australia, according to the Electronic Transactions Act 1999 (Cth), one can meet the legal requirement for a handwritten signature by using an electronic signature or communication.
There is no requirement under common law for a contract to be in writing and signed. Most contracts can be validly formed electronically, if certain elements of a contract are satisfied. These include: intention to create contractual relations; acceptance of an offer; and consideration. The formation and execution of a valid agreement through electronic means is treated like a paper contract in Australia and international Law
Adobe and Norton Rose Fulbright have a nice summary in their Electronic signatures in Australia: Legal considerations and recommended best practices whitepaper. There is also a nice overview of the issue in the Journal of Law, Information and Science article Tech Neutrality in Australian Signature Law.
This information was sourced from the very helpful Global Guide to Electronic Signature Law: Country by country summaries of law and enforceability.