They told reporters in Cape Town they would take part in the national convention called by Terror Lekota and Mbhazima Shilowa in Gauteng this weekend.
Dexter recently resigned from the SA Communist Party.
Rwexana is also a former deputy secretary general of the ANC Women's League (ANCWL), and is the first sitting ANC MP to resign from the party and from Parliament.
Dexter said he was leaving the ANC with a great deal of sadness, but the ANC had undergone a "transformation" since about 2004.
Personal ambition, revenge, and vindictiveness had become the main driving force of the movement.
"Dishonesty has really become the order of the day. Most alarming has been the peddling of many lies by current ANC leaders in recent times to justify political positions and decisions, and in particular, the election or removal of people to and from political office."
The current ANC leadership was at the forefront of undermining the Constitution, Dexter said.
Rwexana said she too was sad to leave the party, which had been her second home for a long time.
However, "today the ANC is very cold... It depends on which side you are supporting.
"The ANC we used to know is no more. The ANC that taught democracy in South Africa is no more... that taught respect to each, respect to the elderly, is no more.
"There's hatred and anger in the ANC [now]. If you have a different view, you are no longer regarded as a member of the ANC. You are regarded as someone who is anti-ANC," she said.
Speaking at the same briefing, Shilowa said work for the convention was progressing well and it was hoped to release the programme and list of speakers on Thursday.
All political parties in Parliament had been invited to attend, as
well as business, trade unions, and individuals, he said.
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