The offer price represents a premium of about 9.9 percent over Genesco's Friday stock closing price of $49.60 on the New York Stock Exchange.
The deal, expected to be completed in fall 2007, would add to Finish Line's net income in the first full year after closing, the athletic shoe and apparel retailer said in a statement.
The deal is expected to generate about $15 million to $20 million in annual cost savings beginning in the first full year of operations, the company added.
Genesco , a shoe and hat retailer, had recently rejected a sweetened takeover bid of $1.2 billion from rival Foot Locker
Finish Line said it does not see significant changes to the workforce due to the acquisition and expects to fund the deal through a combination of about $11 million in cash on hand and up to $1.6 billion in financing.