Smith has made just five Premier League appearances for the Cherries since joining from Liverpool in 2016. He didn't play a single minute of league football last season, spending most of it sidelined with a hip injury.
His lack of regular game time saw him dropped from the Australian squad and he has now moved to the United States so that he can put himself back in contention and add to his 19 caps.
The Sounders, who won the MLS in 2016, are currently 8th in the Western Conference and 13th in the overall table with 22 games played. General Manager Garth Lagerwey hopes that Smith can help them move up the table.
"Combined with his background, Brad’s significant speed and versatility on the flanks make our team immediately better for the stretch run of the season," Lagerwey said.
"We believe he can help our club continue its climb up the table and into the MLS Cup Playoffs."
Smith's loan contains the option of a recall in January if Bournemouth find themselves in the midst of an injury crisis.
Former Fulham and Tottenham player Clint Dempsey is the most famous player currently on the books at the CenturyLink Field.