Hoyte is an England youth international and, having made a handful of appearances for his parent club, now finds himself on a stage where he can progress for a sustained period of time.
"This is a part of the process," Rodgers told Watford's website.
"When you are at the big clubs, you have to have a career before your actual career as such.
"You'll have seen it over the course of the years, the likes of Ashley Cole when he was at Arsenal; initially he spent time at Crystal Palace and got his experience there, came back and got into the team. You need that career before your career."
Hoyte joins the likes of Liam Bridcutt at Vicarage Road, making it one Arsenal and one Chelsea loanee respectively in the ranks, as the trickle of talent starts to come into the Hornets' Hertfordshire training base.
"This is a great move for us and we're very privileged," added Rodgers. "I think it is also a sign of the belief that a club like Arsenal has in what we are doing. It's one of the first boys that we've signed here [from Arsenal].
"They know how they develop players, you can see it. They will only let players out to certain clubs and that club has to fit a criterion of which to develop their talent. Thankfully for us they have seen that of us in the early stages. For both it will work out really well.
"He's a terrific talent and hopefully there will be one or two more coming in as well."
Hoyte is a defender who can fill the right full-back spot or even play at centre-half, and comes with some great attributes, which Watford fans will hope to see in the coming months.
"There's many attributes I like," said Rodgers of his new charge.
"If you're talking about physical attributes I like players to be mobile, I like them to be fast, but certainly not in every area of the team because you need intelligence in a lot of the areas.
"I like technicians, people who are comfortable on the ball. There are many attributes that make up the players, but if we're going to play the way I want us to play - and we've got a hell of a long way to go - then I need people who are going to be comfortable to have the ball.
"He's a boy who's very, very quick. He's aggressive and competitively strong for a young guy and he understands tactically his role.
"He will have had the comforts of Arsenal but this is a great stage for him to come and progress the next part of his career."