"I love the (Pirates) movies, but part of the reason Paul and Rhett are so interesting is that we want to give it a kick in the pants. And that's what I've tasked them with."
Depp's last "Pirates of the Caribbean" was "Dead Men Tell No Tales" in 2017, which was the lowest performing of the five films.
Speaking about his exit, Beattie said: "I think he's had a great run. Obviously, he's made that character his own and it's become the character he's most famous for now.
"And kids all over the world love him as that character so I think it's been great for him, it's been great for us, so I'm just very, very happy about it."
He added: "I think Jack Sparrow will be his legacy. It's the only character he's played five times, it's the character he dresses up in to visit children in hospitals, it's what he'll be remembered for.
"Before Jack Sparrow came along, (Depp) was considered this kind of quirky, independent actor that made these really cool little Tim Burton films but he was by no means a movie star and a lot of people thought we were crazy for casting him at the time.
"Because he wasn't a proven commodity; you know, a big movie star. And we were making a big movie and we were putting this quirky, independent actor in the middle of it and people thought we were crazy."