In a statement read out by his campaign manager Ahmad Ghnaim on Sunday, the West Bank Fatah leader said he wanted to act in the national interest and back Abbas who is the official candidate for the dominant Palestinian faction.
"I again stress my support to brother Abu Mazin [Abbas], the nominee of the movement who is a dear friend and somebody who deserves the position of president.
"I wish him every success in his mission on the road to achieving freedom, the return [of refugees], independence, peace and national democracy."
Al-Barghuthi had been under massive internal and international pressure to withdraw from the campaign, after his candidacy threatened to split Fatah down the middle and derail the US-sponsored Middle East peace process.
The 45-year-old leader was handed five life sentences in June for his alleged part in deadly anti-Israeli attacks. Al-Barghuthi denies the charges.
He angered and astonished Fatah's leadership on 11 December when he announced his candidacy just hours before the close of nominations.
He has since been threatened with expulsion from Fatah and the Israeli government has made it clear that they would not contemplate his early release from prison.
US Secretary of State Colin Powell has also called his nomination problematic, while European donors have made behind-the-scenes threats to slash aid if he were to become head of the Palestinian Authority.
Abbas is now the clear favourite
to succeed Yasir Arafat
While al-Barghuthi is seen as the father of the intifada, Abbas has been an outspoken critic of the militarisation of the Palestinian struggle against Israeli occupation.
In his statement, al-Barghuthi insisted that Abbas remain committed to "the national principles", demanding among other things that he campaign for the creation of a Palestinian state with east Jerusalem as its capital and for the release of all Palestinian prisoners.
He also urged the Palestinians "to hold on to the option of intifada and resistance and to combine it with negotiations".
Al-Barghuthi's withdrawal leaves the path clear for 69-year-old Abbas to sweep to victory next month.
Polls had been showing him running neck and neck with al-Barghuthi who remains hugely popular on the Palestinian street.
Islamic resistance movements Hamas and Islamic Jihad have announced that they are boycotting the presidential election.
Both organisations oppose the 1993 Oslo autonomy accords which paved the way for the Palestinian Authority.
"By nominating himself, Marwan delivered a message reminding everybody that Palestinians are still under occupation and running elections in such circumstances is not a natural situation"
Al-Barghuthi's campaign manager
Al-Barghuthi's change of heart came after several visits to his prison cell in recent days by some of his closest supporters, his wife, Fadwa, and Ghnaim.
Ghnaim said that al-Barghuthi's initial candidacy had managed to advertise the plight of Palestinian prisoners being held in Israeli prisons.
"By nominating himself, Marwan delivered a message reminding everybody that Palestinians are still under occupation and running elections in such circumstances is not a natural situation," he said.