In a phone call on Thursday the US president spoke of his pride in the space agency’s achievement.
Perseverance touched down in a crater after a seven-month flight and a descent described by Nasa as “the seven minutes of terror”.
It is designed to seek out signs of biological life.
Mr Biden watched the landing on television and called Nasa’s Jet Propulsion Laboratory, near Los Angeles, about an hour after touchdown.
Steve Jurczyk, the acting head of the space agency, told a news conference: “His first words were, ‘Congratulations, man’, and I knew it was him. I wasn’t getting caught – only a president could say ‘Congratulations, man’.
“He talked about how proud he was of what we had accomplished.”
Mars rover Curiosity finds evidence of ancient fast-moving streams on surface of red planet
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Mr Biden also asked Mr Jurczyk to “send his regards to Percy”, he added.
Later, the president tweeted a message of congratulations that hailed “the power of science”.
Nasa has described Perseverance as the most ambitious of any American Mars mission, dating back to the Mariner spacecraft’s 1965 fly-by.
Larger and packed with more instruments than the four rovers preceding it, Perseverance is expected to build on previous findings that liquid water once flowed on the red planet, and that carbon and other minerals altered by water and considered precursors to life were present.
Perseverance’s payload also includes demonstration projects that may set the groundwork for future human exploration, including a device to convert the carbon dioxide in Mars’ atmosphere into pure oxygen.
Additional reporting by Reuters