Ishaq Dar, who served as finance minister in Mr Sharif's second administration and again briefly in 2008, would return to the job, Siddiqul Farooq, a spokesman of Mr Sharif's party, the Pakistan Muslim League-N (PML-N), said.
Mr Dar had "all the facts and figures at his fingertips" and will in June present the budget for the next financial year starting on July 1, Mr Farooq said.
Mr Farooq told AFP that the party had secured a "comfortable majority" at the national level and a "two-thirds majority" in Punjab province, where Mr Sharif's younger brother Shahbaz would return as chief minister.
In an astonishing comeback 14 years after he was ousted by a military coup and briefly jailed, Mr Sharif's centre-right Pakistan Muslim League-N (PML-N) is projected to win 130 of the 176 directly elected seats in the national assembly.
Mr Sharif, who has sought to present himself as a pragmatist who can do business with the United States and improve relations with nuclear rival India, won a resounding victory in Saturday's landmark polls.
Mr Sharif's biggest challenges are likely to be fixing the shattered economy, an appalling energy crisis and tackling Islamist militancy.
In Karachi the benchmark index of top 100 shares rose 1.6 percent to 20,232 points in early trade, surpassing the 20,000 mark for the first time as the election results defied analysts' predictions of a weak parliament.
Investors are hopeful of an economic revival under Mr Sharif, whose privatisation policies earned him a good reputation among traders and industrialists during his two previous tenures in the 1990s.
"We have credibility on the economic front, the unprecedented surge in the stock market today is proof," the PML-N spokesman said.
But writing in English-language newspaper The News, analyst and commentator Mosharraf Zaidi expressed disappointment in the choice of Mr Dar, despite calling him "widely respected and highly competent".
If the PML-N goes with the tried and tested, it will be sending the wrong signal to young Pakistanis, that their mocking of the PML-N as 'Purana (old) Pakistan' is not off the mark," he wrote.
Mr Sharif will likely need only the estimated 27 independents and his proportion of seats reserved for women and minorities, to secure a majority in the first democratic transition in a country accustomed to long periods of military rule.
The outgoing Pakistan People's Party suffered a crushing defeat, collapsing from 125 to 33 seats, according to newspaper projections, but enough to emerge as the second largest party and likely to go into opposition.
Cricket star Imran Khan, who promised a "tsunami" propelling him into power, appeared to have slipped into third place on 29 seats - still an astonishing achievement for a party which previously won only one seat in 2002.
US President Barack Obama said Washington was ready to work with Islamabad "as equal partners" and welcomed the transition. India's Prime Minister Manmohan Singh said he hoped to chart "a new course" in relations.
The election commission is expected to finalise the results on Monday night. Mr Sharif will then have up to three weeks to prepare his government before the president summons the national assembly and new MPs are sworn in.
Mr Sharif will then be confirmed as leader of the house and as prime minister, allowing him formally to appoint his cabinet.