The deal is worth $4 million, with Aucoin scheduled to make $1.8 million next season and $2.2 million in 2011-12, a source told ESPN.com's Pierre LeBrun.
Aucoin, 36, had eight goals and 20 assists while playing in all 82 regular-season games in his first year with Phoenix. He also had two assists in seven playoff games and led the NHL with six shootout-winning goals.
Aucoin joined the Coyotes after playing for Calgary, Chicago, Vancouver, Tampa Bay and the New York Islanders. He has 116 goals, 248 assists and 683 penalty minutes in 933 NHL games.
Information from The Associated Press was used in this report.