Adding the attribute splitStatements="true" to the sql tag resolved the issue. Thanks to the tip provided by @siggemannen.

Updated code

<changeSet author="me" id="poc" runAlways="true" runOnChange="true" >
 <sql splitStatements="true">
  BEGIN
      DECLARE @MyVariable INT;
      SET @MyVariable = 10;
  END;
 </sql>
</changeSet>