Woods has the option to name a fourth assistant captain prior to the competition at The Royal Melbourne Golf Club.
Couples has served as the U.S. captain three times (2009, 2011 and 2013) and was an assistant captain in 2015 and 2017. He is also a four-time participant in the event.
"To return to one of my favorite venues, Royal Melbourne, is going to be a real treat," Couples said in a statement. "The fans in Australia really know their golf and create an unbelievable atmosphere for the players, so I'm excited to return and help this team win."
Johnson is a first-time captain's assistant. He competed in four Presidents Cups, including three as Woods' teammate (2007, 2009 and 2013).
"Having competed with Tiger in the Presidents Cup in the past, I've always admired the pride he takes in these team events," Johnson said. "I'm thrilled he's chosen to trust me with this important role, and I look forward to doing my part to help the team succeed."
Stricker was the victorious captain for the U.S. side in 2017, leading the Americans to a 19-11 victory at Liberty National Golf Club in Jersey City, N.J. He was also an assistant in 2015 and a five-time participant, most recently in 2013.
"Stricks was an incredible leader in 2017 and I took a lot away from the way he served as captain that I hope to emulate in Melbourne," Woods said. "We have always shared a high level of trust and mutual respect, which will be important in helping us guide this team."
Held biennially since 1994, the Presidents Cup is a competition between a team from the United States and an international team representing the rest of the world, minus Europe.
The Americans have won the last seven trophies and hold a commanding 10-1-1 overall record against the internationals.
--Field Level Media