The free offer applies to online pre-orders through Telstra's Web site, but is only applicable to plans $80 and above.
Telstra's $80 Every Day Connect plan for the Galaxy Note 3 attracts an $8 monthly handset charge for a total of $88 per month over 24 months.
The plan includes $800 worth of calls and MMS messages, unlimited SMS messages and 1.5GB of data per month.
Telstra will also sell the Galaxy Note 3 for $7 a month on its $100 plan ($107 per month), and for $6 a month on its top $130 plan ($136 per month).
The Galaxy Gear smartwatch is a "companion device" that will initially only work with the Galaxy Note 3 smartphone, and the Galaxy Note 10.1 2014 Edition tablet. It is valued at $369.
The free Galaxy Gear offer ends on Thursday, 17 October, unless it is withdrawn earlier by Telstra.
The Galaxy Note 3 is also available through Optus, Vodafone and Virgin Mobile in Australia, and Vodafone bundles the Galaxy Gear on a select range of plans for an increased monthly price.