Biblical, English and Irish; NT Matthew 10:3.The origin is obscure but it is probably from Greek, meaning possibly "gift of/given by God". See Theodore which has a similar meaning.
Thaddeus is one of many Anglicized forms of the Irish Gaelic Tadhg [q.v.], from Gaelic "poet, philosopher". Both share the pet name Tad. Thady is an Irish pet name.