The 78-year-old is seen as a moderate Democrat, and his nomination by President Joe Biden on Friday drew bipartisan praise.
He will need to be confirmed in the Senate before he can take up the role.
Mr Nelson said he was “honoured” to be picked to steer the US space agency, adding that he would “help lead Nasa into an exciting future”.
In a statement, the White House said he was “known because the go-to senator for our nation’s space programme” for several years. “Almost every piece of space and science law has had his imprint,” it said.
The Republican Senator from Florida, Marco Rubio, said: “I cannot consider anyone better to steer Nasa.”
In a statement, Mr Nelson said Nasa’s workforce “radiates optimism, ingenuity and a can-do spirit.” He added: “The Nasa team continues to realize the seemingly impossible as we venture into the cosmos.”
Mr Nelson was a driving force behind Nasa’s Space Launch System (SLS) rocket, which was conceived in the wake of an Obama-era overhaul of the US space programme.
He will succeed Jim Bridenstine, who led the agency for nearly three years under the Trump administration.
Mr Bridenstine earned widespread praise for his efforts to market Nasa programmes – especially, its Artemis venture, which can see astronauts return to the Moon within the 2020s before mounting a mission to Mars.
“Bill Nelson is a superb pick for Nasa Administrator,” Mr Bridenstine said, adding that the previous Florida senator had the “political clout” to collaborate with different government offices also as members of Congress.