Arculus will succeed Lord Spicer, who is retiring on 9 December, as chairman of the trade association.
Arculus has previously been the chairman of Severn Trent and telecoms company O2, before joining the board of Telefonica following its merger with O2.
He also worked for four years as chairman of the Better Regulation Task Force, reporting to the then Prime Minister, Tony Blair.
Commenting on his successor, Lord Spicer said: “It is right that a businessman with such an impressive track record in business and government should lead an organisation representing this vital sector of our nation’s life.”
On being appointed, Arculus said: “This vital industry deserves a clear, strong voice.
“I look forward to getting to grips with the key three-fold challenge of balancing energy security with the low carbon agenda and with bills which people and industry can afford.”
Slade will take over day to day operational running of the organisation, succeeding outgoing chief executive Angela Knight who is leaving at the end of December.
He said: “I am delighted to be able to take up the reins at Energy UK and see the organisation through into a new phase.
“I aim to ensure the value and importance of the sector is fully realised at the highest level.”
Outgoing chief executive Angela Knight added: “The staff of Energy UK know and respect him and he is very well placed to lead the team forward.
“There are big issues to tackle and Lawrence is the right man for the job.”
Arculus and Slade will start their new roles on 1 January 2015.