Anisimov, an 11-year NHL veteran, spent his last four with the Blackhawks. He carries a $4.55-million cap hit over each of the next two seasons, according to CapFriendly.
The 31-year-old hit the 20-goal mark in three straight campaigns before scoring 15 in 78 games with Chicago in 2018-19.
Chicago acquired Anisimov from the Columbus Blue Jackets as part of the Brandon Saad trade in 2015. The Russian played three years with the Jackets after being included in the deal that sent Rick Nash to the New York Rangers in 2012.
Smith, who's also 31, had spent all 11 of his pro seasons with the Senators, who drafted him 79th overall in 2008. He contributed 28 points in 70 games with Ottawa this past campaign.
He also has two years left on his current contract, but at a cap hit of $3.25 million.