His resignation comes after he refused to retract his comments in which he accused party leader Julius Malema and his deputy, Floyd Shivambu, of financial mismanagement and of accepting a donation from VBS Mutual Bank.
In a 35-point letter, Rawula indicated his intention to resign from the party.
"Let the history judge me, both in terms subjective and objective realities, If I have betrayed the revolution I will take any punishment that comes by my way (sic).
"I subscribe to the notion that, 'society does not perish because of bad people but society perishes because good people have decided to keep quiet until death'.
"Let the society judge me for taking this long to speak but in mitigation of my sentence, I HAVE FINALLY SPOKEN.
"I will now listen to your press conference with peace as the none member of the EFF (sic)."
Financial audits of last 4 years
In a separate letter ahead of his resignation, Rawula, who was the head of the party's disciplinary commission until recently, told Malema's lawyers that the party would first need to produce its financial audits before he retracts his statement.
"I wish to record that I will not be retracting any post from social media unless your client provides the following evidence against my claims," he wrote to the lawyers.
He asked Malema and the EFF to at least produce the last four years of audited statements for its ABSA, FNB and Standard Bank accounts if it wanted Rawula to retract his statements.
Rawula is also demanding that the EFF disclose all the organisational bank and credit card audited statements for the past four years, with all the corresponding invoices and slips.
"Please note, not audited reports submitted to Parliament. I want bank account audited statements," he said.
In the letter to Rawula, Ian Levitt Attorneys who are representing Malema said his allegations against their client were vexatious, misplaced, spurious and untrue.
"We are further instructed that your making these defamatory statements is done deliberately to exact political revenge on our client and the EFF..."
'Should you fail to do so...'
Malema's attorneys demanded that Rawula retract his statement in a form of a public statement, shared via social media.
"Should you fail to do so, we hold instruction to institute further legal action against you," the letter reads.
He told News24 that, over the past four years, he had not been shown a report of the party's finances.
In a social media post on Facebook, Rawula accused Malema and Shivambu of abuse and running a dictatorship.
His claims included that the EFF flouted the constitution in relation to the management of EFF funds.
Rawula said he never accused Malema of stealing money from VBS bank, but that he rather claimed Malema admitted that the EFF received money from VBS.
"The EFF president must prove that an admission to receiving VBS money, which is the subject of corrupt activity, is not rendering the EFF complicit to unlawful activity under his leadership."
In November 2018, journalists from the investigative unit Scorpio reported that the EFF received more than R1.8m in illicit VBS funds flowing through two fronts.
The report said an additional R430 000 was paid in three tranches towards a luxury Sandown property where Malema lived. Scorpio reported the property was bought by and registered in the EFF's name.
The party has denied the allegations.
DM
CAPE TOWN, SOUTH AFRICA – FEBRUARY 12: EFF leader Julius Malema during day 1 of the 2019 State of the Nation Address (SONA) 2019 debate at the National Assembly on February 12, 2019 in Cape Town, South Africa. Members of Parliament gathered to question President Cyril Ramaphosa address, which took place on February 07. Ramaphosa is due to respond on February 14. (Photo by Gallo Images / Sowetan / Esa Alexander)