"We have reached a two-year agreement ... with technical director Vicente del Bosque," Besiktas said in a statement to the Istanbul stock exchange.
The club said it had agreed to pay del Bosque 1.75 million euros ($2.16 million) for his first year and 2.25 million euros for his second.
Del Bosque earlier told Spanish daily El Pais he had agreed to take over at Besiktas, where he will replace Romanian Mircea Lucescu who resigned last month to move to Ukrainian club Shakhtar Donetsk.
"It was a good and attractive option," Del Bosque said. "I am keen to get to know the Besiktas squad and see if the team needs strengthening or not. They have promised me there will be some new signings."
The 53-year-old, who travelled to Istanbul on Monday, said he would be taking the whole of his former Real Madrid coaching team with him to his new club.
"After four very intense seasons working together at Real Madrid we are all really keen to get back to work," he said.
Del Bosque has been out of work since he was discarded by Real at the end of last season after leading the team to two European Cups, two league titles and the World Club Cup.
"He said he was considering bringing footballers from Spain to fill the necessary spots," Besiktas spokesman Reha Muhtar told reporters after the signing.
Real Madrid sacked Del Bosque's successor Carlos Queiroz last month after the team ended the season without a trophy for the first time in five years, appointing former player Jose Antonio Camacho as his replacement.
Club president Florentino Perez admitted that he had made a mistake in appointing Queiroz, but stood by his decision to discard Del Bosque.
Perez later told a Spanish radio station that he planned to offer Del Bosque the chance to return to the club to work with the youth teams.
Del Bosque's agent Pedro De Felipe said that he had received no formal offer from Perez and that, in any case, the former Real Madrid player had preferred to continue as a head coach.
After establishing a nine-point lead at the top of the Turkish first division before the winter break, Besiktas slumped to finish a distant third, earning a place in the UEFA Cup.
Lucescu resigned as Besiktas coach on May 18 after two years in charge during which time he led them to the 2003 league title.
