The Icelandic hitman failed to recapture his striker's role last season and would have fallen further behind in the pecking order following the signing of Andriy Shevchenko.
However a move to the European champions is no step down for the ever-popular attacker and Chelsea-mad wishes him and his family all the best in their new adventure in Spain.
Eidur is expected to sign a four-year deal when his passes his medical.
Gudjohnsen cut a sad figure at the end of Chelsea's final home game of the season when the boys celebrated winning the title again.
For those who were there, one of the biggest cheers of the day was reserved for Eidur's two young boys who dazzled the crowd with some wonderful skills at the Shed end.
One mazy run and strike by his eldest deserved the raputous reward it got as it hit the back of the net.
Goodbye Eidur, you will always be welcome at the Bridge