Spending has risen from 4.92-trillion naira proposed by Jonathan's team, which is led by Finance Minister Ngozi Okonjo-Iweala, who has been praised by economists for her fiscal prudence.
But Parliament usually wins budget disputes.
"Following consultations and an agreement between the executive and the legislature on the 2013 Appropriation Bill, President Goodluck Jonathan today signed the Bill into law," a statement from the presidency said.
"As part of the understanding reached with its leadership, the observations of the executive arm ... will be further considered by the National Assembly through legislative action."
Africa's second biggest economy and top oil producer is growing in popularity as an investment destination, offering the promise of high economic growth and a consumer market of 160-million people.
But investors remain wary of the government's tendency to squander oil revenues through a combination of reckless spending and corruption.
Global oil price
The budget was based on an assumption of a $79 per barrel budget oil price, higher than the $75 per barrel proposed by Jonathan and up from $72 for this year's budget.
Any money earned from oil over and above the benchmark price is deposited into a savings facility called the excess crude account. Any increase in the benchmark price therefore reduces savings and makes Nigeria less resistant to oil price shocks.
According to economists, the global oil price is at almost the same level as it was a year ago – leaving little justification for increasing the benchmark by $7 a barrel.
But lawmakers, who have been unhappy about delays in their allowances set out in the 2012 budget and who want more money freed up for their constituencies, were unlikely to accept such a slight increase in the benchmark price.
The budget assumes oil production of 2.53-million barrels per day, up slightly from 2.48-million barrels per day in the 2012 budget and at the top end of actual output this year.
It also assumes economic growth in 2013 will be 6.5%, inflation 9.5% and assumes an exchange rate of ₦160 to the dollar.
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