The two firms also agreed on an additional performance-based payment of up to $1.15bn in cash and equity.
Assurance uses advanced data analytics to enable an extensive network of live agents to offer customised solutions to potential clients.
“Assurance accelerates the strategy and growth potential of Prudential’s financial wellness businesses, bringing us closer to more people across the entire socio-economic spectrum to better serve the full picture of their needs,” said Charles Lowrey, chairman and chief executive at Prudential.
The agreement will see Assurance become a wholly-owned subsidiary of Prudential under the US business division.
Michael Rowell, co-founder and chief executive of Assurance, said the company “was founded to protect and improve the personal and financial health of every individual”.
Prudential expects the acquisition to be modestly accretive from 2020.
Following the acquisition, Rowell will remain in his role and Michael Paulus will stay as president.
Rowell will report to Andrew Sullivan, who will become executive vice president and head of US business at Prudential.
The business is not connected with UK international financial services group Prudential plc.