Dyche is excited by the competition the pair will bring to Turf Moor.
“It's been a relatively quiet summer across the board in terms of the big deals, and we've been spinning plates in the background, so we are delighted to get two in so early," the Clarets boss said.
“That means they have more time to work with the group and get used to what we do as a unit.
“They are two different players, but with good experience and know their way around the Premier League.
“Erik has had around 170 Premier League games, but we wanted that new challenge for Charlie Taylor, who has done ever so well.
“It's all about getting that competitive element across the board and Jay and Erik will both bring that.
“We don't carry massive numbers and I don't want to carry massive numbers, but we have to carry the right quality within that and we are getting back there."
On Rodriguez's return, Dyche also said: “We have been linked with him over the past couple of years and things sometimes hold deals up, or get in the way, but the time was right, I think.
“Even from a business point of view, it's a pretty good deal overall for a very good player.
“He's proved that over the past couple of years and shown he still has goals in him. But he's also got that competitive instinct to play in a team that wants to compete.
“We want the in-house competitive edge, not just on a matchday, and I definitely think Jay will bring that to the strike force.
“He's been gone a while, but from his history with the club Jay knows all about us. I think he will be someone who can build into what we do here and hopefully enjoy it and be successful."