The Sydney-based insurer, Australia's biggest property and casualty insurer, will add $1.45 billion to its annual sales with the purchase.
The move to buy Winterthur US comes after QBE bought US specialist insurer Praetorian Financial Group and the firm will sell $625 million worth of shares to help fund the two deals.
Frank O'Halloran, QBE Group chief executive, said: "Winterthur US gives us a strong footprint in western, mid-west and north-east US states for small to medium property and casualty business through a large base of independent agents. By contrast, the Praetorian acquisition announced in December will more than double the size of our US specialist insurance program business."
He added: "The acquisition of Winterthur US meets QBE's acquisition criteria; in particular earnings per share accretion in year one. Subject to no unforeseen circumstances, we anticipate profit after tax of $160 million from Winterthur US in the first full year before the cost of funding and synergies."
Axa's decision to sell Winterthur US follows the firm's strategic review that was announced last year.
The deal is expected to close in the second quarter of this year.