He will be replacing Rt Rev Nigel Stock who is retiring after four years in the role.
Rev Tim's new duties will include supporting the Archbishop of Canterbury's work in the House of Bishops, General Synod and the Archbishop's Council.
He will also be involved in the Lambeth Conference 2020 and take on the role of Bishop to the Forces.
Rev Tim has served as the Bishop of Truro since 2009. During his time as bishop, he co-chaired an inquiry into foodbanks. He and his wife Sian have two children.
Rev Tim said: "It will of course be a real sadness to leave Cornwall. However I am very much looking forward to working with the staff at Lambeth, and thinking about how we continue to embed Archbishop Justin's priorities of prayer, evangelism and reconciliation into the life of the Church of England and the Anglican Communion.
"I am particularly interested in the Archbishop's emphasis on spirituality and prayer, and seeing how the incredible work of Thy Kingdom Come continues to flourish."
The Archbishop of Canterbury, Justin Welby said: "I am delighted to be welcoming Bishop Tim to Lambeth Palace. He brings a wealth of experience to the role. He already has extensive knowledge and understanding of the College and House of Bishops, and a heart for those on the margins of society, who are often overlooked. His work on Feeding Britain demonstrates his range of ability and skill in bringing people together."