It will pay $69 (£37) for each Amerus share.
The company, owner of the Norwich Union brand, said the takeover of Amerus would boost the UK firm's presence in the US.
Aviva will also take on around £328m of the Iowa-based company's debt.
The business will trade under the Aviva name and the company anticipates annual savings of around £24.5m. Richard Harvey, Aviva's chief executive, said: "Amerus is a well-managed, innovative and fast-growing business. This acquisition establishes a leadership position within a key segment of the world's largest long-term savings market."