How do you say welcome in the German language?

Welcome home is Willkommen zu Hause in German. This would usually be sufficient as it implies that the person was away for a longer time.

Welcome home from your trip is Willkommen zu Hause aus Ihre Reise.

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Almost, but it should be von Ihrer Reise or the more familiar (informal) form of von Deiner Reise

A less stuffy way of saying welcome home is Willkommen daheim