The 30-year-old Velazquez was promoted from Villarreal's third team to take charge of its B team midway through last season when the Spanish club shuffled around its coaching staff after a poor start in the topflight.
Velazquez acknowledged his youth could be held against him.
"I understand that people can have certain doubts, but capability doesn't come with age, rather with training, a desire to work and on reflecting that each individual draws from his own experiences in life," he said.
"Football is football and our motto is very clear: work, work, and more work."
Villarreal's relegation was confirmed in the closing minutes of the final round, leading to the exit of Miguel Angel Lotina, its third coach of an injury-plagued season.
The club came to an agreement on June 6 with Manuel Preciado to replace Lotina. But the former Sporting Gijon manager died the following morning at the age of 54.
"Life goes on and eventually we had to start again," said Villarreal president Fernando Roig. "Of all the options we thought that the best, the most appropriate and the definitive one was that of Julio Velazquez as Villarreal's new coach. We are going to put all our resources and all our team at his disposal with the goal of returning to the first division."
