Howard has been first-choice at Goodison Park since arriving from Manchester United, initially on loan, in 2006.
The United States international's last deputy, Jan Mucha, provided little in the way of a challenge, making just two appearances in three years before his contract expired this summer.
However, Robles, who worked with Roberto Martinez while on loan at Wigan last season, has arrived on a five-year deal with a view to being Howard's long-term successor.
"In order to go on and achieve great things as a club, you need to have quality in numbers," said Howard.
"I think that's part and parcel of football nowadays. I don't think anyone's fearful of competition, I don't think there are any issues. You just get on with your job.
"I think if you have anything about you, you know your best is good enough.
"You put forward the effort and I don't think that has ever been a problem here."