Bishop David takes over the role with immediate effect, succeeding the Bishop of Leicester, Tim Stevens, who was Convenor for nearly six years and retires as a diocesan bishop in July.
The role involves coordinating the work of the 26 bishops in the House of Lords.
Archbishop Justin Welby said: “I am delighted that Bishop David has agreed to take on this important position.
“As the lead bishop in the House of Lords, the Convenor is relied upon to speak on my behalf and that of all the Lords Spiritual, often engaging with the leaders of other benches across the House on complex and detailed legislative issues.
“Bishop David brings great qualities to the role and will be a vital bridge between the Church and the political world at Westminster.
“In recent years those bishops who have served in Parliament have been fortunate to benefit from the wisdom and dedication of Bishop Tim and the Lords Spiritual owe him a huge debt of gratitude, as he hands over the Convenorship to Bishop David.”