He said BP's board would meet to discuss restoring the dividend in the coming months, in an interview with the BBC
BP stopped paying out money to shareholders following the oil disaster in the Gulf of Mexico.
Dudley, pictured, will formally take over from Tony Hayward as BP's chief executive on Friday.
"The board will get together and talk before the end of the year about restoring a dividend in some form in the first quarter," he said.
"Its obviously for the board to decide, [but] from what I see happening in the performances of the businesses, i believe we will get there."
His plans for restoring the dividend will be encouraging news for shareholders.
Last year, BP paid out about £7bn in dividends.
It was the single biggest dividend payer in the FTSE 100 list of leading companies.
Dudley also pledged to make BP "a good compelling investment for shareholders".