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The legislation would amend the Constitution, and would need to be ratified by three-fourths of the states within seven years after passage in Congress to be enacted.
"In my lifetime, I have seen two elections where the winner of the general election did not win the popular vote," she said in a statement, noting former Vice President Al Gore's electoral loss in 2000. "When all the ballots are counted, Hillary Clinton will have won the popular vote by a margin that could exceed two million votes, and she is on track to have received more votes than any other presidential candidate in history except Barack Obama."
"This is the only office in the land where you can get more votes and still lose the presidency," she continued. "The Electoral College is an outdated, undemocratic system that does not reflect our modern society, and it needs to change immediately. Every American should be guaranteed that their vote counts."
As of Tuesday, Clinton led Trump by roughly 900,000 votes, with some votes in Democratic strongholds still outstanding. Prior to Clinton and Gore, just three times in presidential history had a nominee lost while winning the popular vote. Grover Cleveland in 1888, Samuel Tilden in 1876, and Andrew Jackson in 1824 are the only other three to lose the presidency in that fashion.
With Michigan yet to be called for either candidate, Trump leads Clinton 290-to-232 in the Electoral College.
While he praised the Electoral College following his win, saying it puts more states into play, he tweeted in 2012 following Republican nominee Mitt Romney's loss, that the system was a "disaster for democracy."
Boxer said she agreed with that sentiment in her statement.
"I couldn't agree more," the California Democrat wrote. "One person, one vote!"