Tierney will earn $2.8 million in the first year and $4.2 million in the second.
The 26-year-old was a restricted free agent who had a salary arbitration hearing scheduled for Nov. 8.
He's coming off a two-year pact that carried a cap hit of $2,937,500 - a deal he inked with the San Jose Sharks.
The Keswick, Ontario-born center collected 11 goals and 37 points over 71 games with the Senators this past season, his second with Ottawa. The club acquired him from San Jose in the Erik Karlsson trade in September 2018.
Tierney played four campaigns with the Sharks, who drafted him 55th overall in 2012.