The Blues forgotten man moved to Stamford Bridge in 2015 from Augsburg for £14million under ex-manager Jose Mourinho and went on to make 23 appearances in his first season.
Rahman,24, fell out of favour at Chelsea and was sent back to the Bundesliga on loan at Schalke where he has been for the last two-and-a-half years.
But a serious knee injury has hampered his time in Germany and will move to France to kick-start his career.
Reims are in the midst of their own injury crisis and the defender could go straight into the squad to face Marseille on Saturday.
Rahman who has spent most of his career in Germany has 24 caps for Ghana.
The defender will be desperate to get his career back on track with his Chelsea contract set to expire next year.
He could go down as one the worst pieces of business done by the Premier League side since they signed Winston Bogarde in 2000.
The Dutchman was told to leave by incoming boss Claudio Ranieri but refused to go and sat on his £40,000-a-week wages for the entire four years of his contract featuring just nine times.
Meanwhile, Chelsea has been dealt a blow as Leandro Paredes has snubbed a move to Stamford Bridge to join Paris Saint-Germain.
The Argentine midfielder moves to Ligue 1 from Zenit St Petersburg for £35million and will link up with fellow countryman Angel Di Maria in the French capital.
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