The Bulls officially announced Rondo's signing Thursday. The team did not disclose terms of the contract, but the four-time All-Star has previously told The Undefeated's Marc J. Spears that he agreed to a two-year contract worth almost $28 million.
"Jimmy's the youngest, he's the engine here," Rondo told reporters. "It'll be Jimmy, Wade, and then it will be a pecking order."
Rondo, 30, said he's confident he will be able to coexist with Wade, 34, and Butler, 26, in Chicago.
"The main thing is that we have three alphas. There will be three alphas on the team," Rondo told reporters. "Just trying to mesh together and try to make sure we are doing the best thing for the team."
"Playing in Boston, playing with the Big Three, I was able to see how those guys interacted with one another. Knowing that everything doesn't have to be perfect in practice," he said.
"You're going to disagree, but if you all have one common goal at the end of the day and that's to get a W, that's all that matters. Egos go out the window and we all have one common goal."
Wade, who played with the Miami Heat for 13 seasons, announced his intention to sign with the Bulls on Wednesday night.
Rondo replaces former MVP Derrick Rose, who was traded to New York before the draft.
The Associated Press contributed to this report.