The merged bank would be Australia's largest home lender with a market share of 25 percent, and the largest wealth management provider with funds under administration of A$108 billion.
Westpac said it planned to keep the St George brands and branch networks.
St George shareholders will own 28.1 percent of the combined entity and three St George directors will join the Westpac board, including Chairman John Curtis, who will become the Deputy Chairman of the merged group.
The merger is expected to be cash earnings per share accretive for St George shareholders from the first full year of the merger and within three years of the merger for Westpac shareholders.
The tie-up requires regulatory approvals. Westpac is being advised by Caliburn Partnership and St George by UBS.
Both banks' shares were put on a trading halt on Monday. St George shares closed on Friday at A$26.65, down 15 percent for the year, compared with a 7 percent decline for Westpac which closed at A$25.97.