Back has left with immediate effect with chairman Keith Williams stepping up to an executive role and finance head Stuart Simpson assuming an interim CEO position at the Royal Mail (UKPIL) business.
Bonuses to executive directors have also been axed and the postal group will pay staff a £25mln bonus to frontline staff who have worked through the coronavirus crisis.
Those who have been at work since March will receive up to £200 cash.
Royal Mail made the announcement alongside a trading update which revealed revenues had slumped by £22mln in April even with a sharp rise in parcel volumes.
UK parcel traffic rose by 31% compared to a year ago with revenue up 20%, but this was offset by a sharp fall in letters as businesses closed due to the lockdown.
Letter volumes fell by a third with revenue 23% lower.
Costs also rose by £40mln as the mail service used overtime and agency staff to cover absences due to coronavirus.
The rate of UK absence has now fallen to 11% from a peak of over 20%, with fewer than 200 people furloughed.
Saturday deliveries are scheduled to resume on June 13, said Royal Mail, adding the situation at parcels arm GLS is still evolving with a shift from B2B to B2C parcels across all markets in the UK and overseas.
Total liquidity is around £1.8bn.
Rico Back started his career in Royal Mail's parcels operation, General Logistics Systems (GLS) in 1989, and was appointed group CEO in June 2018 when Moya Greene left.
In the statement, Keith Williams said: "Rico Back has made a significant contribution to the evolution of our business over his 20 years with us, particularly in building our international parcels business and developing our group strategy, which recognised the urgent need for change to create a sustainable business for the future."