The figures show Hamas won at 76 seats in the 132-member parliament.
Election officials said Fatah, which has controlled Palestinian politics for four decades, won 43 seats.
Abbas said he will immediately start consultations on a new government, which is likely to be shaped by Hamas.
Hamas led a suicide-bombing campaign against Israel and is formally committed to destroying the Jewish state. Israel has ruled out dealing with Hamas.
Abbas said his program remains based on a peaceful settlement with Israel aimed at establishing an independent Palestinian state with its capital in East Jerusalem.
Earlier today, Palestinian Prime Minister Ahmed Qurei and his cabinet resigned, even before the official results were announced.
(compiled from agency reports)