Carson is due to undergo a medical with Liverpool today before agreeing personal terms on a four-and-a-half-year contract.
Chelsea were willing to offer Carson a lucrative deal over the same period of time but it is understood he felt his opportunities would have been limited behind Petr Cech at Stamford Bridge.
He will become Liverpool manager Rafael Benitez's first signing from outside Spain.
In confirming Carson's move, United spokesman Bryan Morris said: "We wish Scott the very best at his new club. He has proven himself to be a top-class keeper during his time at Leeds United and we are sure he will continue to impress at Anfield.
"His steady nerve in pressure situations and his professionalism on and off the pitch will ensure he has a bright future ahead of him."
Leeds are interested in taking Liverpool's 3rd-choice keeper Paul Harrison on-loan, should Carson complete his move.
They will look to bring in a replacement and it's thought that Harrison is top of their wish list. Harrison caught the eye of Kevin Blackwell during a recent reserve game and he hopes to secure a deal until the end of the season.