Misys, which provides software to the financial services industry, has agreed to be bought by private equity firm Vista in a deal worth £1.27bn.
Vista plans to combine Misys with its Turaz business, which provides trade and risk management software.
Last month, a proposed merger deal between Misys and Swiss firm Temenos collapsed.
In a trading update, Misys said that revenues for the three months to 29 February had fallen by 12%.
For the nine months to 29 February, revenues were 3% lower.
"Our third-quarter results were impacted predominantly by the cautious approach adopted by customers whilst discussions were taking place about the future ownership of Misys, and also by continued challenging conditions in financial markets," said Misys' acting chief executive, Tom Kilroy.
"However, we are confident that sales are being delayed rather than cancelled."
Announcing the takeover deal, Robert Smith, chairman and chief executive of Vista Equity Partners, said he believed "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.
Earlier this month, Misys' largest shareholder ValueAct had announced it was considering making a bid in partnership with CVC Capital.
However, Misys said it felt it was unlikely to get a better offer than Vista's 350 pence per share bid.
"We think this is likely to be the best deal available to Misys and its stakeholders," Mr Kilroy told the Reuters news agency.
"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."
By the close of trade on Monday, shares in Misys were up 24.5p, or 7.4%, at 354p.