Headley, 33, has played in 14 games at first in his career. He does not own his own first base glove, but he plans on picking up one soon.
"He's going to have a crash course on it," Yankees manager Joe Girardi said.
Headley will likely see most of his action against right-handed pitching, as he struggled against lefties. The Yankees traded for right-handed hitting Garrett Cooper last week. Cooper will see a lot of the time at first when lefties are on the mound. Headley is in the third season of a four-year, $52 million deal.
"If this makes our team better, then I'm happy to do it," Headley said. Frazier also had an open-mind to which position he would fill with the Yankees. However, he did have his preference.
"Third base is definitely my first choice," Frazier said.
Frazier also has a first choice for his number. He was handed No. 29 by the Yankees, but he hopes to switch to No. 21.
Growing up in Toms River, where he helped win a Little League World Series, Frazier was not a Yankees fan, but he did root for Paul O'Neill. He said he hopes to talk with O'Neill to see if he could wear No. 21. The number is not retired. It was worn by LaTroy Hawkins at one point, but after fans booed him, he ended up switching his digits.
Frazier, who struck out and was hit on the hand by pitch in his Yankees debut Wednesday, is hitting only .206.
"I think I did need a change of scenery," he said.