Gudjohnsen had got as far as having a medical at West Ham, and his decision to choose Spurs upset West Ham manager Gianfranco Zola, a former Chelsea team-mate of the Icelandic player.
"I am disappointed with Spurs and disappointed with Gudjohnsen. I was expecting good behaviour from him," said Zola.
"They keep telling me that football has got like this right now and I keep saying that when I'm dealing with people, I always expect for the people that I have got in front me to behave in a certain way - with respect. That wasn't the case here."
West Ham have made new strikers a priority in the transfer window, as they look to drag themselves away from the relegation zone.
Benni McCarthy poised to sign from Blackburn for £2.5m and Celtic's Scott McDonald is also on their radar.
Gudjohnsen has won League titles in England, Holland and Spain, and was an unused substitute for Barcelona when they won the Champions League final in 2009.
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