Hoffman, an unrestricted free agent, signed a professional tryout contract with the Blues on Dec. 27. He recorded 59 points (29 goals, 30 assists) in 69 games with the Florida Panthers last season.
In order to play in the regular season, Hoffman will need to sign a standard contract.
Blues General Manager Doug Armstrong said the Blues have been pursuing Hoffman for awhile now.
"We started this obviously months ago when free agency started," Armstrong said. "Mike got into a situation where he wasn't comfortable with some of the offers that he had, so he was willing to look at a shorter-term deal or coming with us on a tryout. Obviously our plans are to get him signed."
Hoffman has played in nine NHL seasons, seven with the Ottawa Senators and more recently, two with Florida. He has scored at least 20 goals in six straight seasons and set a career-high in goals (36) during the 2018-19 season.
With Vladimir Tarasenko (shoulder) unable to start the season and Alexander Steen announcing his retirement, Hoffman could prove to be a perfect fit.
"I knew St. Louis always had a good club and was kind of one of the teams on my radar coming into (free agency)," Hoffman said. "Anything could happen, there's (still) different possibilities, but this was the one that we thought was the best fit and the best opportunity."