The new tool will be open to 100,000 invitees from 1600BST today -- with each nominee allowed to invite a further five people.
The search term "GoogleWave" is one of the top trending topics on Twitter, with users asking other users for an invitation.
Thousands of Twitter users are tweeting statements about the tool, with @MHWD tweeting: "Like many of you I have my fingers crossed for a Google Wave invite!"
Twitter user @mikaelwestmark said: "Looking forward to Google Wave going on public trial today. Anyone with an invitation to share... :)
Google, which allowed people to register their interest in trialling the service earlier this year, announced first public trial on its this morning.
It is believed more than 1m people registered their interest.
Some are suggesting that Google Wave could revolutionise the way people communicate.
Innovations include real-time typing, which allows people to see comment being written character by character, thus enabling the recipient to formulate their answer to a question before a fellow "Waver" has even finished asking it.
Unlike traditional instant messenger services conversations continue even after everyone has logged out. This means that those invited to a Wave conversation can read the message strand in full at a later date.
Wave also allows users to share photos and edit conversations, with a playback facility that allows everyone to see exactly who has edited what and at what time.
This wiki-style feature has been the focus of a great deal of excitement in the blogosphere as it taps into the growing online trend towards collaboration.
The tool also harnesses the growing influence of social networking sites, with a number of applications including Sudoku and Chess. Wave will have a full consumer launch early next year.