"The Labor party has plenty of fantastic choices as leader; I won't be one of them," he told reporters on Sunday.
Mr Weatherill would not put a timeline on the leadership change, but said it would be "sooner rather than later" once the final results of the election are known.
But he said he would remain in the state parliament on the back bench and had no desire to move to Canberra.
"Absolutely not. I can say that with great passion. I have zero ambitions to go into federal parliament."
He said he wanted to focus on representing his seat of Cheltenham, saying the electorate deserved his full attention.
"I'm in an unusual situation where I'm doing it back to front," he said, noting he was appointed to the front bench early in his parliamentary career.
Mr Weatherill said he now wanted to spend more time with his family.
"My immediate future is going to see mum in the nursing home and have a cup of coffee with dad."
South Australia on Saturday voted to bring an end to Labor's 16 year reign in the state, dashing Mr Weatherill's hopes of leading the party to a record fifth term.
Labor is likely to win 18 seats - a respectable result after their lengthy reign.
