Both posted the news on social media Monday, sharing a photo and brief message.
In addition to winning a Grand Slam title 1 ½ years ago, Stephens was the 2018 French Open runner-up and was a member of the championship U.S. Fed Cup team in 2017.
The 26-year-old American is currently ranked No. 8.
Altidore, 29, has scored 41 goals in 110 international appearances since his U.S. national team debut in 2007. He has not played for the Americans since October 2017, when a loss at Trinidad and Tobago prevented them from qualifying for the 2018 World Cup.
Altidore has been with Toronto FC in Major League Soccer since 2015.
Information from The Associated Press was used in this report.