"We who have inherited the space programme will always be in his debt."
Mr Schirra, known as Wally, died of natural causes on Wednesday night at a hospital in La Jolla, California, the space agency said.
There are now only two surviving members of the Mercury Seven astronauts, who became national heroes as the US took on the former Soviet Union in the space race.
'Spacefaring nation'
Mr Schirra, who was born in New Jersey in 1923, joined Nasa in 1959 as a Navy test pilot who had flown combat missions in the Korean War.
On his first space flight he orbited the Earth six times during a nine-hour flight in a Mercury spacecraft, before landing the capsule successfully in the Pacific Ocean.
His third and final space mission, on the Apollo 7 spacecraft in 1968, was the first to lift off after a fire on the launch pad killed three fellow Apollo astronauts a year earlier.
Although Mr Schirra never walked on the Moon, his crew's 11-day 1968 flight was seen as an important step towards making the Moon landing the next year possible.
He resigned from Nasa a year after his final flight and joined CBS News, where he helped cover the Moon landing.
He was known as a colourful personality who liked a joke, as well as a talented pilot and astronaut.
"We shared a common dream to test the limits of man's imagination and daring," Mr Schirra once wrote.
"Those early pioneering flights of Mercury, the performances of Gemini and the trips to the Moon established us once and for all as what I like to call a spacefaring nation.
"Like England, Spain and Portugal crossing the seas in search of their nations' greatness, so we reached for the skies and ennobled our nation."