Misys has agreed to be bought by Vista Equity Partners for £1.27 billion.
The UK financial services software giant, which was also approached by CVC Capital and ValueAct, only a week ago abandoned a proposed merger with Swiss software counterpart Temenos.
Vista said it will combine Misys with its Turaz business, which sells trade and risk management software and was formerly owned by Thomson Reuters.
Robert Smith, chief executive at Vista, a private equity firm, said Misys "has an attractive future that we plan to invest in and grow".
"With the combination of Misys and Turaz, one of our existing portfolio companies, we are creating the global leader in core banking, treasury management, capital markets and enterprise risk management software headquartered in the global banking centre, London," he added.
Misys acting chief executive Tom Kilroy told Reuters that the Vista offer "is likely to be the best deal available to Misys and its stakeholders", adding: "If any other company made an offer, we would of course talk to them, but we think it is unlikely this deal will be bettered."
Kilroy has been Misys chief executive since the departure of Mike Lawrie, who last month announced he was to become chief executive at troubled outsourcing giant CSC.
Angela Eager, research director at analyst house TechMarketView, noted that the CVC and ValueAct bid was "still in play". The bidding team "could come up with an alternative offer - it has until 2 April," she said.
But she added that "Vista is the stronger contender compared to CVC-ValueAct, given its existing investment in the sector".
With Vista being determined to lead in several financial software categories, it would remain "hungry for acquisitions", she said. "The troubled sector is crowded - in addition to Temenos, Infosys and TCS provide banking software, as do SAP and Oracle. Now Vista is emerging as another potential contender."