The report sent DST's shares surging nearly 23 percent on Wednesday, while SS&C's closed up 12.8 percent.
Both stocks jumped to record highs on Thursday, before easing to trade up about 5 percent each.
The deal is Windsor, Connecticut-based SS&C's latest in its quest to build out its financial software expertise that serves banks and the investment industry. It also gets an entry into the healthcare information technology market.
SS&C Chief Executive Bill Stone said in a statement that the combination would better meet the demand for outsourcing in financial services and help its clients address competitive and regulatory pressures.
"SS&C has a long track record of acquiring underperforming businesses, reducing cost, and increasing efficiency to bring performance more closely in line with its average margins," Morgan Stanley's Brian Essex said in a client note.
DST is SS&C's first large deal since its $2.3 billion takeover of accounting software maker Advent Software in 2015. A year earlier, SS&C had bought DST's investment data analytics unit for $95 million.
SS&C said it plans to fund the acquisition and refinance existing debt with a combination of debt and equity. It expects the deal to immediately add to adjusted earnings, before synergies, after closing in the third quarter.
Excluding DST's debt, the transaction is valued at about $5.06 billion, according to Reuters calculations.