In a word, yes. However, we suggest that you should seek your own legal opinion before relying on the information below.
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
United Nations Convention on the Use of Electronic Communications in International Contracts (Electronic Communications Convention) has been ratified by most countries around the world.
Specifically, in the United States, the Electronic Signatures in Global and National Commerce Act (ESIGN) and Uniform Electronic Transactions Act (UETA) provide that a signature will not be denied legal effect or enforceability solely because it is in electronic form.
The UETA states "an electronic sound, symbol, or process, attached to or logically associated with a record and executed or adopted by a person with the intent to sign the record." This is the same definition adopted by ESIGN, which has been adopted in every state except New York, Washington State, and Illinois (and each of those states have their own electronic signatures statute). This act gave as much weight as "wet" signatures (handwritten with pen and paper).
This information was sourced from the very helpful Global Guide to Electronic Signature Law: Country by country summaries of law and enforceability.