The transaction includes all of SEB's 173 retail branches in Germany, which have about one million customers and about 2,000 employees.
SEB said the deal would allow it to focus on its merchant banking and wealth management divisions.
"The sale of our German banking business will free up capital that will be reinvested in SEB's core strategic growth areas," SEB chief executive Annika Falkengren said in a statement.
SEB said the price of €555 million was at a premium to allocated equity of €420 million. It added transaction costs were estimated at €375 million.
The bank had announced in May it was selling its German retail business because of unsatisfactory profitability. Santander and Italy's Unicredit had reportedly submitted offers, and a deal was expected for the end of July.
Evli Bank analyst Kimmo Rama said the sale was a "positive deal for SEB."
"SEB is more focused on corporate banking in Germany, and the retail branch has been loss making for some time. In the low margin German retail sector, economy of scale is necessary and thus Santander is a good fit," he told Dow Jones Newswires.
SEB is Sweden's third-biggest bank in terms of market capitalisation and employs about 21,000 people worldwide.
SEB acquired its German retail banking business in 2000 and had planned to sell it in 2008, but the transaction was suspended because of the global financial crisis.
In early trade on Monday, SEB's shares were down 0.72 percent to 45.60 kroner on a Stockholm Stock Exchange down 0.43 percent.