"I'm excited to be playing in games sometime this week, and I can't wait to get back with the big league club," Ellsbury said in a statement.
Ellsbury has been out more than five weeks with a right knee sprain. He will begin his rehabilitation in Tampa, Florida. If all goes well, he could be in the Yankees' lineup after the team returns home following its West Coast trip. The Yankees face the Tampa Bay Rays on Friday in the Bronx.
Yankees manager Joe Girardi said he thinks "it is possible" Ellsbury could be back Friday.
Ellsbury, 31, was hitting .324 with a homer, six RBIs and 14 stolen bases in 37 games when he last played on May 19.
Before the Yankees made the announcement about Ellsbury's plans, the outfielder completed one final test running in front of Girardi and Yankees personnel before Sunday's game against the Astros at Minute Maid Park. Ellsbury appeared to be running normally.
The Yankees were 22-18 when Ellsbury went on the disabled list. In his absence, heading into Sunday, they were 19-16 without him.
New York signed Ellsbury to a seven-year, $153 million contract before the 2014 season.