Smith, 31, had nine goals and a career-high 19 assists for Ottawa last season. He has two years left on his contract at $3.25 million annually.
Anisimov, 31, had 15 goals and 22 assists in 78 games for the Blackhawks last season. He had 77 goals and 78 assists across the past four seasons in Chicago.
His contract has two years left and carries a $4.55-million cap hit annually, so the Blackahwks will get some salary relief with this deal.