The MLS team announced the moves on Saturday, a day before its home opener against D.C. United.
Obekop has played in seven games with the Red Bulls over the last two years. The Cameroonian's option was not picked up after the 2014 season. He spent the 2015 preseason with the Red Bulls.
A first-round pick in the 2013 MLS Supplemental draft, Bustamante appeared in four regular-season games as a rookie. He did not appear in 2014 after undergoing season-ending surgery in August.