US Soccer confirmed Andonovski as Ellis' successor on Monday, with the former FC Kansas City and Reign FC boss - who has coached in the NWSL for the past seven seasons - "honored" to land the position.
"It's a huge honor and I'm very excited to get started with this group of players and staff as we work towards continued success for this program," he said in a statement.
"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."
Andonovski has experience of coaching USWNT veterans Megan Rapinoe and Becky Sauerbrunn.
The 43-year-old's first game in charge will come against Sweden on November 7.