Swisher, 36, worked with outfielders Monday during his first day, which came three days after announcing his retirement as a player.
"I never have to worry about an 0-for-4 again," Swisher said with a smile. "It's great to be back."
A-Rod is set to make his initial appearance Tuesday.
"He's going to work with our players," Yankees manager Joe Girardi said. "Dispense knowledge that he has about how to play the game when he talks to the young kids, some of the expectations about how to deal with it. All the things Alex did well."
Rodriguez and Swisher also were guest instructors with the Yankees instructional league team last fall.
"The fact that he's giving back to the game and is involved in the game, that doesn't shock me," Girardi said.
Rodriguez, 41, hit 696 home runs during a 22-year career that ended when he was released by the Yankees last August. Rodriguez hit 351 homers over 12 seasons with New York.
Slowed by knee injuries the past several years, Swisher appeared in 76 games with Atlanta and Cleveland in 2015. He played in 55 games last season for the Yankees' Triple-A Scranton/Wilkes-Barre team, then ended his season in July when his second child was born.
Jacoby Ellsbury, excused for the birth of his child, is due in camp Tuesday. Greg Bird, who missed all of last season following shoulder surgery, homered off Giovanny Gallegos in a simulated game. Aaron Judge hit a pair of balls hard during the simulated game and minor league LHP Justus Sheffield displayed an impressive changeup during live batting practice.