Although Crewe MAD do understand that another club is involved it seems that Varney and his agent have decided on the South East club and a three year deal will be signed with the London based club.
The club will net a fee of £1.6m as Varney's previous club Quorn are entitled to 20% sell on.
Varney who has had a remarkable season, netted 17 goals in the league and ended up Crewe's top goal scorer ahead of Nicky Maynard.
Although Varney signed a new contract during 2006-2007 tieing him to the club until 2009 he has always been linked with numerios teams including Preston North End, Derby County, Newcastle United, Aston Villa and Portsmouth.
Varney who signed for £50k back in March 2003 was seen as a hot prospect and it was not until last season he made a name for himself by scoring 17 league goals and also scoring a well taken goal against Man United in the Carling Cup.
The clubs managemnt had hoped to keep Varney until Jaunuary 2008 but with Charlton's offer it seems that Varney has played his last game in a Crewe shirt.
Meanwhile the club hope to tie up the signing of Eugene Bopp from League Two outift Rotherham United for a nominal fee.