"It was a beautiful day. Simple and sweet," the actor tells PEOPLE in a statement. "I wish them everything that love has given us."
Carey also shared his joy on Twitter Wednesday night. "My Jane is a married women. days ago her and my new son in law alex got hitched,” he wrote. "The day was simply perfect... lots of love there.. :)"
In the spring, the star will become a grandfather as well: Jane, 22, is due to give birth to her first child in March. "I am very excited," he said in July. "Jane is going to be a great mom."
Jane is Carey's daughter with his first wife Melissa.