Andonovksi, 43, moves into the job after spending several years coaching in the National Women's Soccer League. He was head coach at Reign FC -- Megan Rapinoe's current team -- for the 2018 and 2019 seasons.
He won two championships during earlier stints with FC Kansas City, where he coached between 2013 and 2017, twice winning coach of the year honours.
"We are thrilled to welcome Vlatko to the US Soccer family," United States Soccer Federation (USSF) president Carlos Cordeiro said.
"As one of the most accomplished coaches in the NWSL history, he's proven he can help world-class players reach their peak, inspire his teams and win championships.
"He is widely respected by players and leaders across our soccer community, and he has the work ethic and winning mentality to guide the greatest women's soccer program in history into their next era of success."
Andonovski's appointment takes immediate effect, meaning he will oversee the USA's final two games of 2019, against Sweden and Costa Rica in early November.
Those games will be preparation for qualifying games for the 2020 Olympics in Tokyo, where the US are hoping to regain their crown.
"I'm very excited to get started with this group of players and staff as we work towards continued success for this program," Andonovski said.
"All of the talented coaches and players that have come before have built a legendary tradition of excellence and I'm committed to working very hard to continue to move this program forward."
Under his immediate predecessor Ellis, the United States won back-to-back World Cups in 2015 and 2019.