Wal-Mart Stores Inc
Wal-Mart said in a filing that Cornell, 50, will receive a signing bonus of $1 million.
Cornell replaces Doug McMillon, who became president and CEO of Wal-Mart International on February 1.
The shares in Wal-Mart, one of the recession's best performing retailers, closed down 2.9 percent at $47.51 on the New York Stock Exchange.
Private equity firms Bain Capital and the Blackstone Group control Michaels, a seller of arts and crafts supplies.
(Reporting by Lisa Baertlein; Editing by Andre Grenon)