Comey said the compromise is the closest he will get to a public testimony.
A judge had been set to issue a ruling on Comey's request to quash the subpoena and halt congressional proceedings - a request that has never previously been granted by a judge in the United States.
Republican Rep. Bob Goodlatte, the committee's retiring chairman, issued the subpoena to Comey the week of Thanksgiving, requiring his testimony in a closed setting during the final weeks of Republican control of the House.
The detente ended yesterday with Comey agreeing to testify privately, but retaining the ability to speak publicly about his testimony.
"Mr. Comey will join us for a closed-door transcribed interview later this week", the statement said.
The Republican-led inquiry has been lambasted by Democrats as a partisan effort to undermine Special Counsel Robert Mueller's investigation into Russian interference in the 2016 USA election.
Washington pays respects to Bush as he lies in state at Capitol
Martin's Episcopal Church until Thursday morning when he will be eulogized during a funeral at the church. McGrath has been sharing photos throughout the week of how the nation is honoring Bush 41.
Trump fired Comey past year on the grounds that Comey had mishandled the Clinton case, with both then-Attorney General Jeff Sessions and Deputy Attorney General Rod Rosenstein sending memos expressing agreement with the decision.
The Kremlin has denied meddling in the US elections, and Trump denies colluding with Moscow, repeatedly calling the Mueller probe a political "witch hunt" with no basis in fact. He also predicted Comey would be making the rounds on television news and discussing his testimony in detail.
Based on the agreement, Comey was withdrawing his legal motion, and the committee would withdraw its subpoena, Kelley said.
They have also claimed that the Federal Bureau of Investigation made missteps when it applied for a warrant to place former Trump campaign adviser Carter Page under surveillance.
Comey was sacked by U.S. President Donald Trump in May 2017, followed closely by the appointment of special counsel Robert Mueller, who's leading the wide-ranging Russian Federation investigation.
But the hearing is one of several planned by House Republicans in the lame duck session, before Democrats assume the House majority in January, which will focus on the activities and investigations of Clinton.
In exchange for agreeing to testify, the committee will drop the subpoena.