Cunha had already been suspended as speaker in May by the Supreme Court, at the request of the attorney general, who accused him of obstructing justice and hiding millions of dollars in bribes in Swiss bank accounts.
Then last month, the congressional ethics committee voted to strip him of his congressional seat. Although resigning as speaker, he still hangs on to the seat, but could be voted out by the plenary in coming weeks.
Cunha, who has been widely compared to the character Frank Underwood in the TV series "House of Cards," teared up Thursday as he announced his resignation.
"Only my resignation will put an end to the instability," he told journalists during brief comments carried live around the country.
With Cunha spearheading efforts, congress voted overwhelmingly in April in favor of launching an impeachment trial against Rousseff.
With the Senate also voting in favor of a trial a month later, Rousseff was suspended for up to 180 days to defend herself
against allegations she broke budgetary laws when she tried to hide a budget shortfall ahead of re-election in 2014.
"I am paying a high price for having started the impeachment process
. I have no doubt that the main reason for my removal lies in the conduction of this impeachment of the removed president," Cunha said Thursday.
He has been accused of benefiting from a massive bribery scheme involving the state-run oil company Petrobras. The corruption investigation has already brought down some of the country's top political and business leaders.
If congress votes him out, Cunha loses partial immunity from prosecution offered to members of congress and high-ranking politicians.
"I will continue to defend my innocence and that I told the truth," he said.
The final decision in Rousseff's impeachment trial will come after the 2016 Olympic Games
end on August 21.
Vice President Michel Temer
, who belongs to the same party as Cunha, stepped in as acting president and will take over permanently if Rousseff is impeached.
On Thursday, Cunha wished him luck.