Mukherjee, the candidate of the ruling Congress-led alliance, is a respected conciliator, and as head of state he may play a role in who governs India after the general election due in 2014.
The president oversees the formation of a new government when no party wins a clear majority, and most observers predict a close result in 2014 due to the poor economic outlook and the struggles of the current Congress administration.
The outcome of the presidential vote will be announced on Sunday, but Mukherjee, 76, has far more support than his rival, former parliamentary speaker P.A. Sangma, a state legislator for a tribal constituency in the remote northeast.
"There is no permanent equation in India's coalition politics and if Mukherjee becomes the president then his art of negotiation will be put to the test," T.K. Tripathi, a leading political analyst and author, told AFP.
"He can be the kingmaker in this age of complex coalition politics."
The new president will succeed Pratibha Patil, India's first female president, who took a low-profile and strictly detached approach to her five years in the job.
Mukherjee was until last month the finance minister at the heart of a government that has been beset by policy paralysis, rebellious coalition partners and corruption scandals since winning re-election in 2009.
He has also endured heavy flak for the recent sharp fall in economic growth and a growing sense of domestic and international pessimism about India's future after years of rapid development.
Amid such uncertainty, Congress faces a major challenge in keeping enough coalition allies on board to push through much-needed reforms, and the party is already braced for a tough battle in the 2014 polls.
The main opposition Bharatiya Janata Party (BJP), which is supporting 64-year-old Sangma for president, is also unlikely to secure a clear win in national elections, meaning regional parties could hold the balance of power.
Congress scored one victory on Wednesday when the Trinamool Congress party, which has been the ruling coalition's most troublesome partner, reluctantly agreed to back Mukherjee.
"Every party is scouting new partners to be able to form the government," Sanjay Kumar, a political analyst at the Centre for the Study of Developing Societies think-tank in New Delhi, told AFP.
"It is in this turbulent scenario, Mukherjee as a president will be able to steer the ship of the state. He is a trouble-shooter."
Under the constitution, the prime minister holds most executive power, with the president chiefly employed to welcome foreign dignitaries and helping -- if necessary -- in the formation of governments.
The president can also return some bills to parliament for reconsideration.
Indian presidents are chosen by an electoral college comprising MPs from the federal parliament's two houses and from the state legislatures.
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