WASHINGTON — Michael D. Cohen, President Trump’s former personal lawyer who implicated him in a scheme to pay hush money to two women claiming to have had affairs with him, said on Thursday that he had agreed to testify before a House committee next month and give “a full and credible account” of his work for Mr. Trump.

Mr. Cohen’s decision to appear before the House Oversight and Reform Committee on Feb. 7 sets the stage for a blockbuster public hearing that threatens to further damage the president’s image and could clarify the depth of his legal woes. Mr. Cohen, a consigliere to Mr. Trump when he was a real estate developer and presidential candidate as well as informally when he was president, was privy to the machinations of Mr. Trump’s inner circle and to key moments under scrutiny by both the special counsel, Robert S. Mueller III, and federal prosecutors in New York.

He could soon share many of them on national television under oath. But potential constraints emerged almost immediately on Thursday when the committee’s chairman warned that Mr. Cohen most likely would be barred by Mr. Mueller from discussing matters related to Russia.

“In furtherance of my commitment to cooperate and provide the American people with answers,” Mr. Cohen said in a statement, “I have accepted the invitation by Chairman Elijah Cummings to appear publicly on Feb. 7. I look forward to having the privilege of being afforded a platform with which to give a full and credible account of the events which have transpired.”