Misys said it was recommending a 350 pence a share cash offer from Vista, a private equity group which has been targeting deals in software and will combine Misys with Turaz, a provider of trade and risk management software.
Misys last month agreed to merge with its rival Temenos, but the Swiss company walked away after the two sides failed to firm up a deal.
Misys was in takeover talks last summer, reportedly pitched at 400 pence a share.
Since then it has suffered tough conditions in its core banking software market, and it said on Monday that revenue in the year to the end of the third quarter fell 3 percent, after a plunge of 12 percent in last three months.
Misys said the holders of about 22 per cent of its shares had already backed the Vista offer.
The group's largest shareholder ValueAct had said it was teaming up with CVC Capital partners to consider a bid, although analysts questioned whether it was a tactic to drive up the price of any Vista offer.