Last month Shittu, who has one international cap to his name, nearly joined Rangers for £1.5m, but the move broke down over personal terms
Watford boss Aidy Boothroyd was philosophical about the sale. He told BBC Three Counties Radio: "I knew he was going to go because of where we find ourselves financially.
"But I'm pretty sure I will be able to bring some players in now."
Shittu becomes the second big money departure from Vicarage Road this summer following the £2m sale of Darius Henderson to Sheffield United.
But Boothroyd said: "That's all part of a club like Watford at this moment in time. We have to sell. I want to be in a position as a manager where I can trade, and I can't even bring in loan players at present.
"So we need to make sure we get Danny packed off and say thanks very much for all that he has done - and I mean that genuinely - but you can't deny a player the chance to play in the Premier League, and you can't deny me the chance to get some players in."
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