The 35-year-old Redden was placed on waivers this week by the New York Rangers, who bought out the final two years of his contract on Thursday.
Also on Friday, the Blues released 35-year-old defenseman Colin White, who was brought in for a tryout earlier this week. White is three games shy of 800 over 12 NHL seasons. He played in 54 games for the San Jose Sharks last season after 11 seasons with the New Jersey Devils.
Redden, who spent the past two seasons with Connecticut of the AHL, had five goals and 35 assists in 156 regular-season games with the Rangers over two seasons after he signed a six-year, $39 million deal to leave Ottawa.
Under the new labor deal, Redden will earn a pro-rated $3.341 million this season plus two-thirds of the $5 million he was set to earn next season. In 994 career NHL games over 13 years, Redden has 106 goals and 344 assists.
"Wade is a solid two-way defenseman," Blues general manager Doug Armstrong said Friday. "We believe his experience will complement and add stability to our defensive core."