The Atletico Madrid striker has stated that he wants to represent the reigning world and European champions at international level, despite featuring in two friendlies for Brazil, which is the country of his birth.
Del Bosque has said that he welcomes Costa's decision to represent Spain.
"He [Costa] is a noble and good guy," Del Bosque told Marca.
"If he wants to come, it will be with all our blessings. With him we have a striker for many years."
Costa has scored 10 goals in eight appearances for Atletico Madrid this season.