The United States international has been the Toffees' established number one since arriving from Manchester United, initially on loan, in 2006.
His last deputy Jan Mucha, provided little in the way of a challenge to Howard, making just two appearances in three years before his years before his contract expired this summer.
However, Robles, who worked with new Everton manager Roberto Martinez while on loan at Wigan last season, has arrived on a five-year deal with a view to the 23-year-old 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," the 34-year-old American told the club's website.
"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."
Martinez's new signings, he has also recruited former Wigan players striker Arouna Kone and Antolin Alcaraz and Barcelona youngster Gerard Deulofeu, have already had an impact on the squad.
"We've brought four new signings in already and it's been impressive. There's been a momentum with us so far," said midfielder Leon Osman.
"Now we're all together and have got the rest of our international lads back, we've got our full squad and we can start to look forward even more.
"It's about how quickly now we can all understand what the new manager wants and how he wants us to play.
"That's different from being comfortable on the ball. We need to be comfortable in the mind as well."
The Toffees are well into their pre-season training and have already played two friendlies against Austria Vienna and Accrington Stanley and make the short trip to Blackburn on Saturday before heading to the United States for three games.
"Pretty much everything we've done so far on the field has been with the ball," added Osman.
"All the running has been with the ball and it's something we don't usually do.
"I've loved it. You'd be surprised how hard it is with the ball though.
"It's because you're concentrating on the running and keeping the ball under good control at the same time.
"We worked long and hard in Austria, three sessions a day.
"As far as being comfortable and composed on the ball goes we've certainly got players capable of being that. That's a positive."