New York also received a second-round pick in the 2022 NHL Draft.
Buchnevich, who can become a restricted free agent July 28, scored an NHL career-high 48 points (20 goals, 28 assists) in 54 games this season.
"I'm excited to have Pavel join our group," Blues general manager Doug Armstrong said. "... He's got good size at 6-3. He is a left shot, can play the right side. He's scored in the League recently. He's 26 years old. A player that obviously we control for a year and would like to sign long term. ... A very good penalty killer too, a very underrated penalty killer. So he's going to touch all aspects of our game and he's at a good age as we continue to retool this roster, and I think he's a good piece for us."
Selected by New York in the third round (No. 75) of the 2013 NHL Draft, Buchnevich has scored 195 points (79 goals, 116 assists) in 301 regular-season games and has one assist in eight Stanley Cup Playoff games.
"I think he's a definite top-six forward," Armstrong said. "You look at the minutes that he averaged last year (18:44), where he finished in scoring on the Rangers (fourth), I think he's just starting to come into his own."
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Blais scored 15 points (eight goals, seven assists) in 36 regular-season games this season and one goal in four playoff games. The 25-year-old has one season remaining on the two-year, $3 million contract ($1.5 million average annual value) he signed with St. Louis on April 15, 2020.
"As you can see with some of the moves we've made, we're trying to reshape and get a different look in our bottom six," New York GM Chris Drury said. "I think he brings a lot of size, a good physical edge. I think he's got some offensive upside. In the minutes he's played in the past, he's had good production. Like Barclay [Goodrow], he's another guy that walks into our room with a ton of playoff experience and also has a Stanley Cup ring."
Selected by the Blues in the sixth round (No. 176) of the 2014 NHL Draft, Blais has scored 35 points (17 goals, 18 assists) in 119 regular-season games and eight points (three goals, five assists) in 27 playoff games. He won the Stanley Cup with St. Louis in 2019.
"I want to thank Sammy Blais for his contributions to our organization over the last number of years," Armstrong said. "[I] wish him nothing but the best of luck and success with the Rangers."
New York previously acquired Goodrow and defenseman Nick DeSimone in separate trades July 17.
Goodrow, a forward acquired from the Tampa Bay Lightning for a seventh-round pick in the 2022 draft, agreed to terms on a six-year contract Thursday. Financial terms were not disclosed.
DeSimone was acquired from the Vegas Golden Knights with a fourth-round pick in the 2022 draft for forward Brett Howden.
NHL.com senior writer Dan Rosen and correspondent Louie Korac contributed to this report