"Mr. Meadows has been engaging with the Select Committee through his attorney. He has produced records to the committee and will soon appear for an initial deposition," Thompson said in a statement Tuesday.
"The Select Committee expects all witnesses, including Mr. Meadows, to provide all information requested and that the Select Committee is lawfully entitled to receive. The committee will continue to assess his degree of compliance with our subpoena after the deposition."
Meadows' move goes off a referral for charges of criminal contempt of Congress, such as former Trump Adviser Steve Bannon is facing.
George Terwilliger, Meadows' attorney, proved to CNN in a statement that there is an agreement between the committee and Meadows about how information can be delivered.
He also said that both parties are free to engage on a certain set of topics while dealing with information that could end up collapsing under executive privilege.
CNN reports that the agreement may be short-lived if the sides don't agree on the privileged information question.
The news broke as Trump's lawyers were debating in a federal appeals court in Washington, D.C., on Tuesday about whether the former President can assert executive privilege. The White House established in October that President Joe Biden denied Trump's bid to invoke executive privilege on documents related to the Jan. 6 attack on the Capitol.
"As we have from the beginning, we continue to work with the Select Committee and its staff to see if we can reach an accommodation that does not require Mr. Meadows to waive Executive Privilege or to forfeit the long-standing position that senior White House aides cannot be compelled to testify before Congress," Terwilliger said in his statement to CNN. "We appreciate the Select Committee's openness to receiving voluntary responses on non-privileged topics."
Several sources told CNN that Meadows is confirming that he's ready to cooperate with the committee. However, the extent to which he's willing to cooperate is still unknown, and even though the agreement has been reached, criminal contempt charges could still be filed if he tries to keep too much information.
"It's not incorrect to say he has cooperated to some extent, but he hasn't completely fulfilled his obligation and we need to see what happens," a source told CNN. "But Meadows doesn't want to be held in contempt."
Bannon, meanwhile, faces two counts of contempt of Congress for failing to testify and to turn over documents after the committee issued a subpoena to him.