Ms Johnson calculated rocket trajectories and Earth orbits for Nasa’s early space missions.
She was portrayed in the 2016 Oscar-nominated film Hidden Figures.
The film tells the story of African-American women whose maths skills helped put US astronaut John Glenn into orbit around the Earth in 1962. Ms Johnson verified the calculations made by new electronic computers before his flight.
Nasa administrator Jim Bridenstine described Ms Johnson as “a leader from our pioneering days”.
“Ms Johnson helped our nation enlarge the frontiers of space even as she made huge strides that also opened doors for women and people of colour in the universal human quest to explore space,” he said in a statement.
“Her dedication and skill as a mathematician helped put humans on the Moon and before that made it possible for our astronauts to take the first steps in space that we now follow on a journey to Mars.”
Ms Johnson was awarded the Presidential Medal of Freedom in 2015. Then-US President Barack Obama later cited her in his State of the Union address as an example of the country’s spirit of discovery.