Anaggellō means to announce, declare, or bring back a report — to relay information from one party to another. Appearing about 14 times in the NT, it is a compound of ana (up/back) and aggellō (announce/messenger), suggesting the bringing back of news or the full declaration of something. It is used of reporting back to authorities, declaring divine truths, and the proclamation of the gospel.
John 4:25 provides a fascinating use: the Samaritan woman says the Messiah will "announce all things" to us — a recognition that the Christ's role includes divine revelation and disclosure. Jesus in John 16:13–15 uses anaggellō for the Spirit's ministry: "He will tell [anaggellei] you what is yet to come... he will receive from me what he will make known to you." The Spirit's work is to faithfully declare what belongs to Christ. Acts 20:20,27 use it for Paul's complete declaration of the gospel — holding nothing back.