Avery, 27, had a career-high 48 points (18-30) and added 174 penalty minutes in 84 games with Los Angeles and the Rangers. The Pickering, Ont., native earned $1.1 million last season.
"We are pleased to have Sean under contract and are looking forward to him returning with the same passion and enthusiasm he brought to our team last year," Rangers president and general manager Glen Sather said in a statement. "He is a terrific competitor, who we expect to play a significant role in a successful season."
The five-foot-10, 195-pound winger has 50 goals, 84 assists and 913 penalty minutes in 322 career games with Detroit, Los Angeles and New York.
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