Parenteau, 29, is coming off a career-high 67-point season for the Islanders and was seeking a significant raise from the $1.25 million he earned last season with New York.
He recorded 18 goals and 49 assists in 80 games with the Islanders in 2011-12 and totaled just two points less than highly coveted Devils free agent Zach Parise.
He played for the New York Rangers during the 2009-10 season before signing as a free agent with the Islanders in July 2010. He has 41 goals and 129 points in four NHL seasons with three teams.
Avs general manager Greg Sherman says Parenteau "is a skilled winger who will instantly improve our offense."
Information from ESPN.com's Pierre LeBrun and The Associated Press contributed to this report.