"This path is not the one that I would've chosen for Missourians or my colleagues", House Speaker Todd Richardson (R) said at a press conference.
The special session required three-fourths of the members of the senate and three-fourths the members of the house.
Per the state Constitution, after the legislative session there are only two ways for the legislature to return: the governor calls a special session, or the House and Senate have a majority vote to hold a special session.
No Missouri governor has ever been impeached.
His criminal trial on felony invasion of privacy charges begins May 14, four days before the special session. Two staffers said they abided by Greitens' multiple orders to share the list, which The Associated Press reported yielded nearly $2 million in donations to the campaign.
Greitens' request for bench trial in March was denied. Court documents allege Greitens took a nude photograph of a woman he was having an affair with in 2015 and then transmitted the photo so it could be seen on a computer.More news: United Kingdom baby in legal fight dies
Lawmakers will convene May 18 in a special session to consider impeachment.
The move will mark the first time in state history that lawmakers have called a special session, which are typically called by governors.
Richardson said the session will give lawmakers "the time it needs to conduct a fair, thorough and timely investigation" without being halted by the end of regular session.
The report says a former Greitens' campaign aide testified he was deceived into being listed in an Ethics Commission settlement as providing the charity donor list to Greitens campaign.
The second report, released earlier this week, claims Greitens lied on a campaign disclosure form about a list of donors to his charity, The Mission Continues.
Richardson said he already spoken with retired judges about the process of preparing a potential trial panel. Last month, it released a report with testimony from the woman involved in the affair. It was a wild week in Jefferson City with the spotlight focused on Governor Eric Greitens and his legal problems.
Under Missouri law, any articles of impeachment would be proposed to the General Assembly by the special House committee.