The 52-year-old Glasgow-born peer told Mr Cameron in a letter that he wanted to return to his career in the private sector and "take up other threads of my life and other interests".
He was replaced as Leader of the Lords by Lord Hill of Oareford, who also becomes Chancellor of the Duchy of Lancaster and a member of the Privy Council.
Lord Strathclyde, who is married with three daughters, entered the Lords in 1986.
He is the son of former Glasgow Hillhead MP Sir Tam Galbraith and succeeded to the barony of Strathclyde following the death of his grandfather in 1985.
He has held a number of roles during his time in the Lords including chief whip, Minister for Tourism, Privy Counsellor and leader of the Conservative Party.
Lord Strathclyde was one of the hereditary peers elected to remain in the reformed upper chamber in 1999 and served as opposition leader in the Lords from 1998 until the creation of the coalition Government in 2010, when he was appointed Leader of the Lords.
In today's letter, he said that, when first appointed to Government in 1988 he "never believed it was a career for life".
Lord Strathclyde told the PM: "I started my working life in the private sector and at some stage always hoped to return. I would like to do so now.
"While I have the highest respect for the privilege and duty of public service, I do not see a political career as the cap to everything and would like, while there is still time, to take up other threads of my life and other interests".
Lord Strathclyde said he had always hoped to provide a "smooth handover to a strong successor" and with the prospect of Lords reform now "effectively over" and the Government "beginning to bring recovery and change for the better", he felt that the upper House now needs "a new Leader to see it through different challenges in the years ahead".
In a letter accepting his resignation, Mr Cameron praised Lord Strathclyde as "an outstanding Leader of the Lords", adding: "I entirely understand your desire to pursue other interests."
Mr Cameron made clear that a return to the front line of politics was not ruled out, telling the peer: "I do hope that at some point in future years you will have a further contribution to offer."
Although he only entered Parliament in 2010, Jonathan Hill also has a long history in politics.
He worked in the Conservative Research Department and as special adviser to Kenneth Clarke during the Thatcher administration, then joined John Major's Downing Street policy unit and served as political secretary to the Prime Minister from 1992-94, before moving into public relations.
He was made a peer in 2010 and was appointed minister for schools in the Department for Education. It was widely reported that he attempted unsuccessfully to resign this role in last year's reshuffle. Downing Street said that a replacement as schools minister will be appointed in the coming days.