Nieto is coming off a season in which he scored a career-high 15 goals for the Avalanche. He also had his first career NHL hat trick on Oct. 24 against Dallas.
In the postseason, Nieto contributed three assists during a series loss to Nashville.
General manager Joe Sakic said Nieto brings "speed and offensive depth to our lineup. He adds a lot of energy to our team."
The 25-year-old Nieto was claimed off waivers by Colorado on Jan. 5, 2017. He had seven goals and four assists in 43 games for the Avalanche in 2016-17.
Nieto was originally a second-round pick of the San Jose Sharks in 2011.