Prime Minister Boris Johnson said the outgoing health chief had “led the NHS with great distinction for the past seven years”.
NHS England said Sir Simon on Thursday notified the organisation’s board of his decision to stand down “as planned” at the end of July.
In a separate announcement, Downing Street said the Queen had been pleased to confer a life peerage on Sir Simon following his decision.
He will sit as a crossbencher, according to an NHS England spokesman.
In a statement, Sir Simon said: “Joining the health service in my early twenties was one of the best decisions I’ve ever made, followed three decades later by the privilege of leading the NHS through some of the toughest challenges in its history.
“The people of this country have rightly recognised the extraordinary service of NHS staff during this terrible pandemic, as well as the success of our Covid vaccination deployment.
“As the pandemic recedes in this country, the NHS’s track record in advancing medical progress in a way that works for everyone rightly continues to inspire young people to join one of the greatest causes – health and high quality care for all, now and for future generations.”
Mr Johnson issued his thanks for Sir Simon’s “dedicated service … especially when facing the extraordinary pressures of the past year, and for his huge contribution to our vaccine rollout”.
The health boss is understood to have alerted Lord Prior, chairman of NHS England, last summer about his intention to step down but wanted to see through the coronavirus vaccination programme.
Following the announcement, Lord Prior said the country owed Sir Simon a “huge debt of gratitude”.
Health Secretary Matt Hancock and his predecessor Jeremy Hunt were among those who paid tribute to Sir Simon’s work during his time as NHS England chief.
Mr Hancock said: “Throughout his tenure Sir Simon Stevens has been a steadfast and sage leader for our National Health Service, and that has been especially true during this most testing period in NHS history.
“His leadership has helped NHS staff to overcome unprecedented adversity and keep services open for millions of patients in the face of this global pandemic.”
Commons Health and Social Care Committee chairman Mr Hunt said: “Hiring him remains one of the best decisions I have ever taken.
“He will be remembered for giving the world’s fifth largest organisation strategic direction at a time of great challenge.
“However, the immediate dividend from his leadership has been the superb NHS response to the pandemic: every patient that needed a ventilator or ICU bed got one and we have rolled out the best vaccination programme in Europe. He should feel extremely proud today.”
Sir Simon took up the top post in April 2014, having first joined the NHS in 1988 through its graduate management programme.
Before landing the job, he worked in frontline NHS services and in international healthcare before later taking up work in the private sector.
In the public sector, he advised Tony Blair during his incumbency at 10 Downing Street and also served in the Department of Health for the Labour administration.
Former prime minister Mr Blair said: “I am so proud that someone who worked with me in Downing Street went on to … achieve so much.
“Simon has always been a passionate believer in a publicly funded healthcare system, suitably reformed to take account of changing times.”
NHS England said it would be advertising for his replacement “shortly”, with the aim of having a successor appointed before Sir Simon steps down on July 31.
Labour leader Sir Keir Starmer said: “I want to thank Simon for his extraordinary service to our NHS.
“The NHS Covid-19 vaccination programme under Simon’s leadership has shown the NHS at its best. I wish him well for the future.”