Davenport was appointed head of the EU Delegation to Serbia by EU High Representative for Foreign Affairs and Security Policy Catherine Ashton on Friday. He will take up office after the summer.
The British Embassy said he would cooperate with Serbian officials based on the considerable achievements Serbia had recently made on its road to EU membership.
Davenport's appointment is a reflection of Britain's commitment to the continuation of EU enlargement throughout the Western Balkans, the embassy said.
The term of the current head of the EU Delegation to Serbia, Vincent Degert, expires in August.