French drugmaker Sanofi-Aventis completed its improved $20.1 billion offer for Genzyme, allowing it to begin merging the U.S. biotech firm into its business and add rare diseases to its growth areas.

Sanofi said 84.6 percent of Genzyme's common stock had been tendered, with shareholders receiving $74 in cash and one certificate per share entitling them to future payments if specified milestones tied to several of Genzyme's treatments are met.

To allow remaining Genzyme shareholders to tender their shares, Sanofi has opened a subsequent offer period beginning Monday and ending on Thursday, Sanofi said in a statement.

(Reporting by James Regan; Editing by Vinu Pilakkott)