The drug maker, which began trading on AIM in March 2015, said Jackson will resign at the end of the month while Armstrong has decided not to stand for re-election at the upcoming annual general meeting.
The announcement came as Redx posted a loss before tax of £15.5mln in the year to 30 September, compared to £8.9mln a year earlier, as the group invested heavily in a pipeline of new products.
Its pipeline includes the development of its Porcupine RXC004 treatment for pancreatic, biliary and gastric cancer.
The drug will enter it first in-human studies following a clinical trial application (CTA) submission in the second quarter.
Redx is also developing leukaemia treatment BTK RXC005 and plans to make an investigational new drug application and CTA towards the end of 2017.
"Redx has created a world-class capability in small molecule drug discovery in oncology and immunology," said chief executive Neil Murray.
"We have a strong research engine that continues to deliver an innovative pipeline, but we must now shift our focus towards developing our key portfolio assets, specifically our Porcupine and BTK programs for hard to treat diseases."
Redx ended the year with net cash of £5.8m, compared to £9.4mln the previous year. The company generated other operating income of £2.4mln, down from the prior year’s £2.6mln, which included fund grants from the Business, Energy and industrial Strategy.
The company said it looks forward to 2017 with confidence to future developments of the business as it transitions from a pre-clinical to a clinical stage and undergoes a restructuring.
As part of the restructuring, the company plans to cut jobs by 60% to 86 positions, which will help achieve cost savings of about £4.2mln.