Mr Farage said his “political ambition has been achieved” with the UK having voted to leave the EU.
He said the party was in a “pretty good place” and said he would not change his mind about quitting as he did after the 2015 general election.
Leading UKIP was “tough at times” but “all worth it” said Mr Farage, who is also an MEP. He added that the UK needed a “Brexit prime minister”.
Mr Farage said the party would campaign against “backsliding” on the UK’s exit from the EU, saying he planned to see out his term in the European Parliament – describing his party as “the turkeys that voted for Christmas”.
He said his party’s “greatest potential” lay in attracting Labour voters, adding that he would not be backing any particular candidate to replace him.
“May the best man or woman win,” he said.
Mr Farage said he would “bury the hatchet with anybody” including UKIP’s sole MP Douglas Carswell, who tweeted an emoji picture of a smiley face as the leader’s resignation was announced.
The two have repeatedly clashed and tensions rose when they backed rival Leave campaigns ahead of the referendum.