Cohen, who is scheduled to report to federal prison May 6, will also testify in a closed-door hearing with the House Intelligence Committee on Thursday.
The White House has pre-emptively trashed Cohen's testimony, calling him a "disgraced felon."
"Michael Cohen was one of many lawyers who represented me (unfortunately). He had other clients also. He was just disbarred by the State Supreme Court for lying & fraud," Trump said in a tweet on Wednesday.
"He did bad things unrelated to Trump. He is lying in order to reduce his prison time. Using Crooked's lawyer!" he added.
Cohen pleaded guilty to several charges last year in cases brought by the Southern District of New York and special counsel Robert Mueller's office, including financial crimes, lying to Congress and campaign-finance violations linked to hush-money payments given to two women who claimed they had sexual encounters with Trump.
Cohen implicated Trump in his campaign-finance confession. Trump has denied the affairs and all wrongdoing.
— CNBC's Terri Cullen and Mike Calia contributed to this report.