He said he would leave to take up a job in the private sector as he does not see a political career as the "cap to everything".
The 52-year-old also known as Tom Galbraith will be replaced by Jonathan Hill, who was already in the Government as an education minister.
Mr Strathclyde said he was "very sad" to be leaving but his departure represents a "new chapter".
Lord Strathclyde was in charge of trying to steer reforms of the House of Lords through the upper chamber until they were killed by a backbench rebellion of Tory MPs last year. (© Daily Telegraph, London)