Steen has appeared in 493 regular-season games with the Blues and ranks 11th in club history with 355 points (147 goals, 208 assists). He had NHL career-highs with 33 goals in 2013-14 and 64 points in 2014-15.
In 11 NHL seasons, the Winnipeg native has 481 points (197 goals, 284 assists) in 746 NHL games, and 24 point (10 goals, 14 assists) in 51 playoff games.
Steen, who will make $7 million in 2017-18, $7 million in 2018-19, $5.5 million in 2019-20 and $3.5 million in 2020-21, is recovering from offseason shoulder surgery but is on schedule to play in the regular-season opener at the Chicago Blackhawks on Oct. 12.
Armstrong felt that going into the final year of Steen's current contract, which pays him $6.5 million, he wanted to get this deal done as quickly as possible.
"When we talked last year, and even when the season was over, we both said if we could get it wrapped up so it wasn't a distraction going into the season, that would be great," Armstrong said. "We had some conversations when he got back, and he had put a lot of work into trying to get ready for the World Cup. When he wasn't able to pull that off, we had some conversations with his representative here in Toronto at the World Cup and it finished quickly, but it was a four-, five-month process that we went through to get to where we are today.
"It's always nice to have these done before training camp or before the season because it just removes a distraction from Alexander and his teammates."
The fact that Steen is taking a contract with a slightly lower salary-cap charge shows his appreciation for the Blues, who believed in him when they traded for him.
"I don't think I could have seen myself throwing anything on over my shoulders other than a Blue note right now," Steen said. "It takes some time to grow attached like this. For me, it's nothing that I take lightly, and I'm extremely happy that I'm staying here."