The news, which broke late on Tuesday, signals an end to weeks of wrangling that had shaken bond markets. A source in Prime Minister Giuseppe Conte's office said a deal was not expected to be formalised until a meeting of EU commissioners on Wednesday.
After initially refusing to budge on its expansionary budget plans and launching verbal assaults on EU commissioners, Italy's populist government relented last week and submitted a revised plan, including a deficit target of 2.04 percent.
"It is clear that the European Commission doesn't want a harsh confrontation with the Italian government - next year is an election year and it will be delicate," said Sergio Capaldi, fixed income strategist at Intesa Sanpaolo.
The revised deficit figure is down from the original budget target of 2.4 percent of gross domestic product (GDP) in 2019, itself an increase from 1.8 percent this year. The initial proposal was rejected by the European Commision for breaching EU fiscal rules.
Relief that the budget saga may be drawing to a close was evident in the bond market.
Italy's two-year bond yield briefly slid 14 basis points to 0.395 percent, its lowest level since late May -- when Italy was gripped by a political crisis that on May 29 sparked the biggest one-day jump in two-year yields in 26 years.
Five-year Italian bond yields fell to 1.804 percent on Wednesday, the lowest since September, before rising to 1.863 percent and 10-year yields slid 16 bps to 2.78 percent and were last down at 2.84 percent.
The Italian/German 10-year bond yield gap meanwhile briefly touched 252.3 basis points before widening to around 258 bps, the tightest since late September. That spread stood at 268 bps in late Tuesday trade.
Analysts noted that because that spread had come in sharply in the past two weeks on hopes of a budget deal, further tightening was likely to be limited for now.
"This is very short-term relief for Italian bonds. In the medium-term I do not buy the fact that the spread will narrow in a sustainable way," said Capaldi.
Analysts at UniCredit added in a note that "some caution is still warranted."
"First, there are still no details available on the agreement. Second, spreads have come down significantly since mid-November ... which increases the risk of a sell-the-fact reaction. Third, the first months of 2019 will be challenging for Italy from a funding perspective."
January is the busiest month for Italian bond supply and with the European Central Bank withdrawing its stimulus, the bid for Italian bonds may be depleted.
Outside Italy, yields in broader eurozone bond markets crept up but investors were generally sidelined ahead of a US Federal Reserve rate decision later in the day.
Belgian bonds underperformed after Belgium Prime Minister Charles Michael resigned after a no-confidence motion. Belgium's 10-year government bond yield rose three basis points to 0.77 percent.
The Federal Reserve is expected to raise interest rates, but may cut the number of hikes it anticipates next year and signal an earlier end to its monetary tightening in the face of financial market volatility and rising recession fears.